user19: One important thing that Hindus and Buddhists agree on is the law of Karma.  That is, there are certain actions which will lead a person to have a positive experience in future, either in this life or the next, and there are other actions which will lead a person to have a negative experience in future.  And Hindus and Buddhists also agree that ultimately the goal of life is not to just do good Karmas so you can have positive experiences in future, but rather to break out of he whole cycle of Karmas and their consequences.  Buddhists believe that this can be done through the Eightfold Path, and Hindus believe in other means like knowledge of the supreme being.
But my question is about what determines good Karmas and bad Karmas.  Hindus believe that the Vedas (and texts derived from them) tell us exactly what actions constitute good Karma and what actions constitute bad Karma.  But Buddhists reject the Vedas, so my question is, how do Buddhists determine what actions are good Karmas and what actions are bad Karmas?  Do Buddhist scriptures discuss how to determine this?
Note that I don't think the answer is "The Eightfold Path", because that's about what's required to break the cycle of Karma and consequence, whereas my question is about what's required to get positive experiences through the law of Karma.  Also, on a side note, do Buddhists simply classify Karmas into good or bad, or do they subdivide these categories further?  Because Hindus believe in a more fine-grained system where different kinds of good Karmas produce different kinds of positive experience.

user471: Please see this answer on karma, rebirth and effects of karma on this life and future lives.
From the Nibbedhika Sutta:

"Intention, I tell you, is kamma. Intending, one does kamma by way of
  body, speech, & intellect.

In Buddhism, intention is the basis for karma. There are some guidelines on removing unskillful thoughts and qualities. The story of the blind elder monk Ven. Chakkhupala in Dhammapada 1 and the story of the hunter's wife in Dhammapada 124 further illustrates this.

Dhammapada 1: All mental phenomena have mind as their forerunner; they
  have mind as their chief; they are mind-made. If one speaks or acts
  with an evil mind, 'dukkha' (suffering) follows him just as the wheel follows
  the hoofprint of the ox that draws the cart.
Dhammapada 124: If there is no wound on the hand, one may handle
  poison; poison does not affect one who has no wound; there can be no
  evil for one who has no evil intention.

It appears that the simplest way to identify unskillful thoughts and actions, is whether they are imbued with the three poisons or not. And for skillful thoughts and actions, it's the opposite.
In the Vitakkasanthana Sutta, we find that unskillful thoughts imbued with desire/ greed, aversion/ hatred, or delusion have to be removed.
In the Vina Sutta:

"Monks, in whatever monk or nun there arises desire, passion,
  aversion, delusion, or mental resistance with regard to forms
  cognizable via the eye, he/she should hold the mind in check.
  [Thinking,] 'It's dangerous & dubious, that path, thorny & overgrown,
  a miserable path, a devious path, impenetrable. It's a path followed
  by people of no integrity, not a path followed by people of integrity.
  It's not worthy of you,' he/she should hold the mind in check with
  regard to forms cognizable via the eye.

And the same applies to the other senses.
You can find a similar discussion in the Aparihani Sutta where it talks about removing "evil, unskillful qualities such as greed or distress".
In the Sacitta Sutta, also teaching us to remove unskillful thoughts:

"If, on examination, a monk knows, 'I usually remain covetous, with
  thoughts of ill will, overcome by sloth & drowsiness, restless,
  uncertain, angry, with soiled thoughts, with my body aroused, lazy, or
  unconcentrated,' then he should put forth extra desire, effort,
  diligence, endeavor, relentlessness, mindfulness, & alertness for the
  abandoning of those very same evil, unskillful qualities.

Detailed classification can be found in the Abhidhamma in the volume called Dhammasangani ("Enumeration of Phenomena"). We can find a classification list in the work The Abhidhamma in Practice by N.K.G. Mendis:

Sa"nkhaaraa is a collective term for the other fifty cetasikas (mental factors). These
  fall into four groups:

Universal mental factors (sabba citta saadhaaranaa)
Particular mental factors (paki.n.nakaa)
Unwholesome mental factors (akusalaa)
Beautiful mental factors (sobhanaa)


You can read the details on this page for the full classification of the 50 cetasikas.
There are also other classifications there like the different types of cittas (momentary states of mind and consciousness) - vipaaka, kusala, akusala, kiriya. They have association with roots (hetu, mula - see below) and feelings (vedana) etc.

There are six roots. Three are kammically unwholesome (akusala); the
  other three may be either kammically wholesome (kusala) or
  indeterminate (abyaa-kata), depending on the type of consciousness
  they arise in. The unwholesome roots are greed (lobha), hatred (dosa),
  and delusion (moha). The three roots which are wholesome in some
  cittas and indeterminate in others are greedlessness (alobha),
  hatelessness (adosa), and undeludedness (amoha). Though these last
  three roots are expressed negatively they have positive
  manifestations. Greedlessness manifests as generosity and
  renunciation, hatelessness as loving-kindness, and undeludedness as
  wisdom or understanding.

The above are only the Theravada texts. There will undoubtedly be additional discussion on this, in the Mahayana texts.
You can find useful info also in Ven. Thanissaro's Kamma: A Study Guide.


OP: I think skillfull vs. unskillful has to do with what will lead you to liberation vs. what will serve to keep you in Samsara.  But my
  question is about what will serve to give you positive experience in
  Samsara vs. what will serve to give you negative experiences in
  Samsara.

Skillful thoughts and actions will give you a positive experience in Samsara and could also lead you to liberation. Unskillful thoughts and actions will give you a negative experience in Samsara.
But liberation requires much more than skillful thoughts and actions. It also requires one to abandon all the fetters.
For e.g. by practising one or more of the Brahmaviharas (loving kindness, compassion, empathetic joy and equanimity) which is skillful, one could obtain the pleasant experience of birth in the heavans. But this is not permanent.

user8157: 
That is, there are certain actions which will lead a person to have
  a positive experience in future, either in this life or the next,

The Pali suttas do not literally state this. The Pali suttas (eg. AN 6.63) state there are three results of kamma: (i) now; (ii) later; (iii) later again. 
For example, the kamma of drinking alcohol has three results: (i) pleasure now; (ii) headache tomorrow; (iii) habit, craving or addiction later. 
Next life kamma is an interpretation rather than a literal reading of the Pali suttas. In the Pali suttas, words such as 'birth' ('jati'), 'death' ('marana'), 'body'('kaya'; group) do not necessarily have a physical meaning. 
The Buddhist commentaries & suttas (somewhere) state how the ordinary person views Dhamma is the opposite to how an enlightened person views the same Dhamma teachings. In the commentaries, this is known as the 'two truths'. The ordinary person reads everything as physical materialism where as the enlightened person reads everything as it really is. Thus, the Buddha does not speak lies when he uses language that can be interpreted in two-ways.
In is not correct to assert Buddhism teaches about past & futures lives because this is not literally said in the original scriptures (although is literally asserted in later scriptures & commentaries). 

And Hindus and Buddhists also agree that ultimately the goal of life is not to just do good Karmas so you can have positive experiences in
  future, but rather to break out of he whole cycle of Karmas and their
  consequences. Buddhists believe that this can be done through the
  Eightfold Path, and Hindus believe in other means like knowledge of
  the supreme being.

The Buddhist idea seemed to exist systematically before the Hindu idea. At least the idea of moksha with Brahma appears to be not mentioned in the Pali suttas, which report discussions with Brahmans who followed the Vedas. While the early Upanishads are not mentioned in the Pali suttas, it appears the ideas in them about moksha seem to be either immature or not widespread at the time of the Buddha.  

But my question is about what determines good Karmas and bad Karmas. Hindus believe that the Vedas (and texts derived from them) tell us
  exactly what actions constitute good Karma and what actions constitute
  bad Karma. But Buddhists reject the Vedas.

The Buddha did not reject anything in the Vedas he agreed was beneficial. The Pali suttas explicitly state the Buddha was a friend of the Brahmans and wished no harm to the Brahmans. When the Brahmans tried to argue (like Jews) they were a chosen or superior caste, born from Brahma's mouth, the Buddha replied if they do bad kamma how can they be superior?; to which the Brahmans agreed. So both Buddha & the Brahmans had respect for good kamma as a determinative factor for a superior 'birth' (status). 

so my question is, how do Buddhists determine what actions are good Karmas and what actions are bad Karmas? Do Buddhist scriptures discuss
  how to determine this?

In Buddhism, the ten skilful kamma are non-killing, non-stealing, non-sexual-naughtiness, honest speech, pleasant speech, cordial-non-divisive speech, beneficial speech, non-greed, non-hatred & non-delusion. Apart from this, there are many other lists, such as in the Sigalovada Sutta. 
In Buddhism, everything is determined on the basis of causing suffering/harm & leading to freedom from suffering/harm, which can be known via personal experience. Refer to the Kalama Sutta.

Note that I don't think the answer is "The Eightfold Path", because that's about what's required to break the cycle of Karma and
  consequence,

Correct.

Also, on a side note, do Buddhists simply classify Karmas into good or bad, or do they subdivide these categories further?

Basically two-categories, namely, wholesome/skilful & unwholesome/unskilful (although there is a sutta with four types: white, black, white-black, neither-white-black). 
Naturally, there are more refined superior good kammas, such as excellent generosity, meditative heavenly jhana, loving-kindness (metta), serving arahants, etc. 
For example, there are many different godly realms in Buddhism, which are the results of different kammas as well as human, animal, ghost & hell birth from different kammas. 
Godly realms represent special attainments, such as worldly wealth, political power or higher spiritual qualities, such as psychic powers. 
Human birth means being moral. 
Animal birth is being immoral, ghost birth is being chronically craving & hell birth is suffering & torture. 

Because Hindus believe in a more fine-grained system where different kinds of good Karmas produce different kinds of positive experience.

Buddhism is an experiential tradition. The degrees of kamma are known in the heart. 

user111: Karma is intentional thought. If the intention is associated with greed, hatred and ignorance, it's bad Karma. If the intention is associated non-greed, non-hatred, non-ignorance it's good Karma.

19: <p>One important thing that Hindus and Buddhists agree on is the law of Karma.  That is, there are certain actions which will lead a person to have a positive experience in future, either in this life or the next, and there are other actions which will lead a person to have a negative experience in future.  And Hindus and Buddhists also agree that ultimately the goal of life is not to just do good Karmas so you can have positive experiences in future, but rather to break out of he whole cycle of Karmas and their consequences.  Buddhists believe that this can be done through the Eightfold Path, and Hindus believe in other means like knowledge of the supreme being.</p>

<p>But my question is about what determines good Karmas and bad Karmas.  Hindus believe that the Vedas (and texts derived from them) tell us exactly what actions constitute good Karma and what actions constitute bad Karma.  But Buddhists reject the Vedas, so my question is, how do Buddhists determine what actions are good Karmas and what actions are bad Karmas?  Do Buddhist scriptures discuss how to determine this?</p>

<p>Note that I don't think the answer is "The Eightfold Path", because that's about what's required to break the cycle of Karma and consequence, whereas my question is about what's required to get positive experiences through the law of Karma.  Also, on a side note, do Buddhists simply classify Karmas into good or bad, or do they subdivide these categories further?  Because Hindus believe in a more fine-grained system where different kinds of good Karmas produce different kinds of positive experience.</p>
 471: <p>Please see <a href="https://buddhism.stackexchange.com/a/8935/471">this answer</a> on karma, rebirth and effects of karma on this life and future lives.</p>

<p>From the <a href="http://www.accesstoinsight.org/tipitaka/an/an06/an06.063.than.html" rel="nofollow noreferrer">Nibbedhika Sutta</a>:</p>

<blockquote>
  <p>"Intention, I tell you, is kamma. Intending, one does kamma by way of
  body, speech, &amp; intellect.</p>
</blockquote>

<p>In Buddhism, intention is the basis for karma. There are some guidelines on removing unskillful thoughts and qualities. The story of the blind elder monk Ven. Chakkhupala in <a href="http://www.tipitaka.net/tipitaka/dhp/verseload.php?verse=001" rel="nofollow noreferrer">Dhammapada 1</a> and the story of the hunter's wife in <a href="http://www.tipitaka.net/tipitaka/dhp/verseload.php?verse=124" rel="nofollow noreferrer">Dhammapada 124</a> further illustrates this.</p>

<blockquote>
  <p>Dhammapada 1: All mental phenomena have mind as their forerunner; they
  have mind as their chief; they are mind-made. If one speaks or acts
  with an evil mind, 'dukkha' (suffering) follows him just as the wheel follows
  the hoofprint of the ox that draws the cart.</p>
  
  <p>Dhammapada 124: If there is no wound on the hand, one may handle
  poison; poison does not affect one who has no wound; there can be no
  evil for one who has no evil intention.</p>
</blockquote>

<p>It appears that the simplest way to identify unskillful thoughts and actions, is whether they are imbued with <a href="https://en.wikipedia.org/wiki/Three_poisons" rel="nofollow noreferrer">the three poisons</a> or not. And for skillful thoughts and actions, it's the opposite.</p>

<p>In the <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.020.than.html" rel="nofollow noreferrer">Vitakkasanthana Sutta</a>, we find that unskillful thoughts imbued with desire/ greed, aversion/ hatred, or delusion have to be removed.</p>

<p>In the <a href="http://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.205.than.html" rel="nofollow noreferrer">Vina Sutta</a>:</p>

<blockquote>
  <p>"Monks, in whatever monk or nun there arises desire, passion,
  aversion, delusion, or mental resistance with regard to forms
  cognizable via the eye, he/she should hold the mind in check.
  [Thinking,] 'It's dangerous &amp; dubious, that path, thorny &amp; overgrown,
  a miserable path, a devious path, impenetrable. It's a path followed
  by people of no integrity, not a path followed by people of integrity.
  It's not worthy of you,' he/she should hold the mind in check with
  regard to forms cognizable via the eye.</p>
</blockquote>

<p>And the same applies to the other senses.</p>

<p>You can find a similar discussion in the <a href="http://www.accesstoinsight.org/tipitaka/an/an04/an04.037.than.html" rel="nofollow noreferrer">Aparihani Sutta</a> where it talks about removing "evil, unskillful qualities such as greed or distress".</p>

<p>In the <a href="http://www.accesstoinsight.org/tipitaka/an/an10/an10.051.than.html" rel="nofollow noreferrer">Sacitta Sutta</a>, also teaching us to remove unskillful thoughts:</p>

<blockquote>
  <p>"If, on examination, a monk knows, 'I usually remain covetous, with
  thoughts of ill will, overcome by sloth &amp; drowsiness, restless,
  uncertain, angry, with soiled thoughts, with my body aroused, lazy, or
  unconcentrated,' then he should put forth extra desire, effort,
  diligence, endeavor, relentlessness, mindfulness, &amp; alertness for the
  abandoning of those very same evil, unskillful qualities.</p>
</blockquote>

<p>Detailed classification can be found in the Abhidhamma in the volume called Dhammasangani ("Enumeration of Phenomena"). We can find a classification list in the work <a href="http://www.accesstoinsight.org/lib/authors/mendis/wheel322.html" rel="nofollow noreferrer">The Abhidhamma in Practice</a> by N.K.G. Mendis:</p>

<blockquote>
  <p>Sa"nkhaaraa is a collective term for the other fifty cetasikas (mental factors). These
  fall into four groups:</p>
  
  <ul>
  <li>Universal mental factors (sabba citta saadhaaranaa)</li>
  <li>Particular mental factors (paki.n.nakaa)</li>
  <li>Unwholesome mental factors (akusalaa)</li>
  <li>Beautiful mental factors (sobhanaa)</li>
  </ul>
</blockquote>

<p>You can read the details on <a href="http://www.accesstoinsight.org/lib/authors/mendis/wheel322.html#cetasika" rel="nofollow noreferrer">this page</a> for the full classification of the 50 cetasikas.</p>

<p>There are also other classifications there like the different types of cittas (momentary states of mind and consciousness) - vipaaka, kusala, akusala, kiriya. They have association with roots (hetu, mula - see below) and feelings (vedana) etc.</p>

<blockquote>
  <p>There are six roots. Three are kammically unwholesome (akusala); the
  other three may be either kammically wholesome (kusala) or
  indeterminate (abyaa-kata), depending on the type of consciousness
  they arise in. The unwholesome roots are greed (lobha), hatred (dosa),
  and delusion (moha). The three roots which are wholesome in some
  cittas and indeterminate in others are greedlessness (alobha),
  hatelessness (adosa), and undeludedness (amoha). Though these last
  three roots are expressed negatively they have positive
  manifestations. Greedlessness manifests as generosity and
  renunciation, hatelessness as loving-kindness, and undeludedness as
  wisdom or understanding.</p>
</blockquote>

<p>The above are only the Theravada texts. There will undoubtedly be additional discussion on this, in the Mahayana texts.</p>

<p>You can find useful info also in Ven. Thanissaro's <a href="http://www.accesstoinsight.org/lib/study/kamma.html" rel="nofollow noreferrer">Kamma: A Study Guide</a>.</p>

<hr>

<blockquote>
  <p><strong>OP:</strong> I think skillfull vs. unskillful has to do with what will lead you to liberation vs. what will serve to keep you in Samsara.  But my
  question is about what will serve to give you positive experience in
  Samsara vs. what will serve to give you negative experiences in
  Samsara.</p>
</blockquote>

<p>Skillful thoughts and actions will give you a positive experience in Samsara and could also lead you to liberation. Unskillful thoughts and actions will give you a negative experience in Samsara.</p>

<p>But liberation requires much more than skillful thoughts and actions. It also requires one to abandon all the <a href="https://en.wikipedia.org/wiki/Fetter_(Buddhism)" rel="nofollow noreferrer">fetters</a>.</p>

<p>For e.g. by practising one or more of the <a href="http://www.accesstoinsight.org/lib/authors/nyanaponika/wheel006.html" rel="nofollow noreferrer">Brahmaviharas</a> (loving kindness, compassion, empathetic joy and equanimity) which is skillful, one could obtain the pleasant experience of birth in the heavans. But this is not permanent.</p>
 8157: <blockquote>
  <p><strong>That is, there are certain actions which will lead a person to have
  a positive experience in future, either in this life or the next,</strong></p>
</blockquote>

<p>The Pali suttas do not literally state this. The Pali suttas (eg. AN 6.63) state there are three results of kamma: (i) now; (ii) later; (iii) later again. </p>

<p>For example, the kamma of drinking alcohol has three results: (i) pleasure now; (ii) headache tomorrow; (iii) habit, craving or addiction later. </p>

<p>Next life kamma is an interpretation rather than a literal reading of the Pali suttas. In the Pali suttas, words such as 'birth' ('jati'), 'death' ('marana'), 'body'('kaya'; group) do not necessarily have a physical meaning. </p>

<p>The Buddhist commentaries &amp; suttas (somewhere) state how the ordinary person views Dhamma is the opposite to how an enlightened person views the same Dhamma teachings. In the commentaries, this is known as the 'two truths'. The ordinary person reads everything as physical materialism where as the enlightened person reads everything as it really is. Thus, the Buddha does not speak lies when he uses language that can be interpreted in two-ways.</p>

<p>In is not correct to assert Buddhism teaches about past &amp; futures lives because this is not literally said in the original scriptures (although is literally asserted in later scriptures &amp; commentaries). </p>

<blockquote>
  <p><strong>And Hindus and Buddhists also agree that ultimately the goal of life is not to just do good Karmas so you can have positive experiences in
  future, but rather to break out of he whole cycle of Karmas and their
  consequences. Buddhists believe that this can be done through the
  Eightfold Path, and Hindus believe in other means like knowledge of
  the supreme being.</strong></p>
</blockquote>

<p>The Buddhist idea seemed to exist <strong>systematically</strong> before the Hindu idea. At least the idea of moksha with Brahma appears to be not mentioned in the Pali suttas, which report discussions with Brahmans who followed the Vedas. While the early Upanishads are not mentioned in the Pali suttas, it appears the ideas in them about moksha seem to be either immature or not widespread at the time of the Buddha.  </p>

<blockquote>
  <p><strong>But my question is about what determines good Karmas and bad Karmas. Hindus believe that the Vedas (and texts derived from them) tell us
  exactly what actions constitute good Karma and what actions constitute
  bad Karma. But Buddhists reject the Vedas.</strong></p>
</blockquote>

<p>The Buddha did not reject anything in the Vedas he agreed was beneficial. The Pali suttas explicitly state the Buddha was a friend of the Brahmans and wished no harm to the Brahmans. When the Brahmans tried to argue (like Jews) they were a chosen or superior caste, born from Brahma's mouth, the Buddha replied if they do bad kamma how can they be superior?; to which the Brahmans agreed. So both Buddha &amp; the Brahmans had respect for good kamma as a determinative factor for a superior 'birth' (status). </p>

<blockquote>
  <p><strong>so my question is, how do Buddhists determine what actions are good Karmas and what actions are bad Karmas? Do Buddhist scriptures discuss
  how to determine this?</strong></p>
</blockquote>

<p>In Buddhism, the ten skilful kamma are non-killing, non-stealing, non-sexual-naughtiness, honest speech, pleasant speech, cordial-non-divisive speech, beneficial speech, non-greed, non-hatred &amp; non-delusion. Apart from this, there are many other lists, such as in the <a href="http://www.accesstoinsight.org/tipitaka/dn/dn.31.0.nara.html" rel="nofollow noreferrer">Sigalovada Sutta</a>. </p>

<p>In Buddhism, everything is determined on the basis of causing suffering/harm &amp; leading to freedom from suffering/harm, which can be known via personal experience. Refer to the <a href="http://www.accesstoinsight.org/tipitaka/an/an03/an03.065.than.html" rel="nofollow noreferrer">Kalama Sutta</a>.</p>

<blockquote>
  <p><strong>Note that I don't think the answer is "The Eightfold Path", because that's about what's required to break the cycle of Karma and
  consequence,</strong></p>
</blockquote>

<p>Correct.</p>

<blockquote>
  <p><strong>Also, on a side note, do Buddhists simply classify Karmas into good or bad, or do they subdivide these categories further?</strong></p>
</blockquote>

<p>Basically two-categories, namely, wholesome/skilful &amp; unwholesome/unskilful (although there is a sutta with four types: white, black, white-black, neither-white-black). </p>

<p>Naturally, there are more refined superior good kammas, such as excellent generosity, meditative heavenly jhana, loving-kindness (metta), serving arahants, etc. </p>

<p>For example, there are many different godly realms in Buddhism, which are the results of different kammas as well as human, animal, ghost &amp; hell birth from different kammas. </p>

<p>Godly realms represent special attainments, such as worldly wealth, political power or higher spiritual qualities, such as psychic powers. </p>

<p>Human birth means being moral. </p>

<p>Animal birth is being immoral, ghost birth is being chronically craving &amp; hell birth is suffering &amp; torture. </p>

<blockquote>
  <p><strong>Because Hindus believe in a more fine-grained system where different kinds of good Karmas produce different kinds of positive experience.</strong></p>
</blockquote>

<p>Buddhism is an experiential tradition. The degrees of kamma are known in the heart. </p>
 111: <p>Karma is intentional thought. If the intention is associated with greed, hatred and ignorance, it's bad Karma. If the intention is associated non-greed, non-hatred, non-ignorance it's good Karma.</p>
