user4749: This blew, and is still kinda blowing, my mind:

"The Buddha never, afaik, used a term that could be translated as
  "rebirth". In fact, the idea of anything being reborn goes against
  orthodox early Buddhist teachings." (from this comment by
  Yuttadhammo)

So... I have always thought of "rebirth" as being a fundamental concept of Buddhism. Sure, it's "real" meaning is debated, but the fact that there is something to it has, in my studies thus far, never been brought into question.
My real question might be something like, "What the heck?!".... But in terms of presenting something here more formal, I ask: If this is the case (and if not, perhaps you can explain why you disagree with Yuttadhammo's assertion), then where did the concept of "rebirth" come from? Why is it a topic of discussion?

user254: the idea of anything being reborn goes against orthodox early Buddhist teachings
In this later comment, yuttadhammo wrote,

the pali word is "upapajjati", which means something like "he arises". No sense of "re-" at all

So that's the distinction that he's trying to make, in the context of that question:

OP is implying that something that has ceased might arise again. This doesn't happen. Talking about rebirth as a theory is fine, as long as we understand that in reality nothing is actually "reborn". It's a poor name for what really happens.

If I look in the Pali dictionary for the word punabbhava cited in Thiago's answer, the dictionary definition is "renewed existence, new birth" rather than "rebirth".
Looking at the root of the word Puna it suggests meanings like "again" but also "tail", "poop", "behind".
That reminds me of this definition of the word akalika (which means 'timeless'), which includes the following paragraph:

It is probably most useful here to go to the ultimate roots: a = no; ka = shit; li = line; ka = shit. The track of scat left by an animal. The hunter sees: This is the track a week old, this is only two days old, this is from yesterday, and here it is now, eating. That would point to the original meaning of the term to be closer to successive than to simultaneity.

So by analogy, "born again" or "living again" might be like "pooping again": i.e. it is "again", "re-pooping", but let's be clear that they're two different poops.
where did the concept of "rebirth" come from
Here are a couple of articles from accesstoinsight:

The Truth of Rebirth starts with,

Rebirth has always been a central teaching in the Buddhist tradition.

This article includes hyperlinks to the suttas.
Does Rebirth Make Sense? doesn't include specific hyperlinks but does say things like,

The teaching of rebirth crops up almost everywhere in the Canon, and is so closely bound to a host of other doctrines that to remove it would virtually reduce the Dhamma to tatters. Moreover, when the suttas speak about rebirth into the five realms — the hells, the animal world, the spirit realm, the human world, and the heavens — they never hint that these terms are meant symbolically. To the contrary, they even say that rebirth occurs "with the breakup of the body, after death," which clearly implies they intend the idea of rebirth to be taken quite literally.


Why is it a topic of discussion?
It's a topic of discussion because if a doctrine of "rebirth" implies there's something (perhaps a permanent self or soul) that "is reborn", then that seems to contradict other Buddhist doctrines.

user111: When you plant a mango seed and a mango plant comes out of it, what do you call it? Rebirth or the resurrection of the parents mango tree? Certainly not! The term 'rebirth' can be used at a conceptual level to tell a story, when we are not really focusing on whether or not there's a self or a soul. But it's inappropriate to use it when you are discussing ultimate realities. 
ex: "Julia went to sleep last night. Julia woke up this morning". 
That's how we tell a story. But there's no 'Julia' in reality. Julia is just a concept. In reality, it is just the five aggregates which is always changing. So the Julia who woke up this morning is not the same Julia who went to sleep last night.

user-1: Bhikkhu Bodhi writes:

The Buddhist term for rebirth in Pali is "punabbhava" which means "again existence". Buddhism sees rebirth not as the transmigration of a conscious entity but as the repeated occurrence of the process of existence. There is a continuity, a transmission of influence, a causal connection between one life and another. But there is no soul, no permanent entity which transmigrates from one life to another.

The word "rebirth" might be inappropriate since it implies something that borns again (and that's unlikely the meaning of what the Buddha meant). I understand this is what yutthadammo was saying. But, for better or worse, it is this english word that has been used to describe the process of "continuous becoming" in buddhism in english.
"With the break up of the body, after death, he/she reappears at ...", that's what we read. As ven. Bodhi said, The difficulty with this is the doctrine of anatta: if no part of our constitution is fixed, we can't talk about something that transmigrates or is reborn.
But at the same time, we can't say the being that died and the one that reappeared are completely unrelated. What has been said is that the "relation" (or, perhaps better, continuity) is the kamma.

"Student, beings are owners of kammas, heirs of kammas, they have kammas as their progenitor, kammas as their kin, kammas a as their homing place. It is kammas that differentiate beings according to inferiority and superiority."
  -- MN 135


4749: <p>This blew, and is still kinda blowing, my mind:</p>

<blockquote>
  <p>"The Buddha never, afaik, used a term that could be translated as
  "rebirth". In fact, the idea of anything being reborn goes against
  orthodox early Buddhist teachings." (from <a href="https://buddhism.stackexchange.com/questions/10067/did-the-buddha-mean-this-by-rebirth/10113#10113">this comment</a> by
  <a href="https://buddhism.stackexchange.com/users/18/yuttadhammo">Yuttadhammo</a>)</p>
</blockquote>

<p>So... I have always thought of "rebirth" as being a fundamental concept of Buddhism. Sure, it's "real" meaning is debated, but the fact that there is <em>something</em> to it has, in my studies thus far, never been brought into question.</p>

<p>My real question might be something like, "What the heck?!".... But in terms of presenting something here more formal, I ask: If this is the case (and if not, perhaps you can explain why you disagree with Yuttadhammo's assertion), then <strong>where did the concept of "rebirth" come from?</strong> Why is it a topic of discussion?</p>
 254: <p><strong>the idea of anything being reborn goes against orthodox early Buddhist teachings</strong></p>

<p>In <a href="https://buddhism.stackexchange.com/questions/10067/did-the-buddha-mean-this-by-rebirth/10113#comment14641_10113">this later comment</a>, yuttadhammo wrote,</p>

<blockquote>
  <p>the pali word is "upapajjati", which means something like "he arises". No sense of "re-" at all</p>
</blockquote>

<p>So that's the distinction that he's trying to make, in the context of that question:</p>

<blockquote>
  <p>OP is implying that something that has ceased might arise again. This doesn't happen. Talking about rebirth as a theory is fine, as long as we understand that in reality nothing is actually "reborn". It's a poor name for what really happens.</p>
</blockquote>

<p>If I look in the Pali dictionary for the word <a href="http://dsalsrv02.uchicago.edu/cgi-bin/philologic/getobject.pl?c.2:1:2929.pali" rel="nofollow noreferrer">punabbhava</a> cited in Thiago's answer, the dictionary definition is "renewed existence, new birth" rather than "rebirth".</p>

<p>Looking at the root of the word Puna it suggests meanings like "again" but also "tail", "poop", "behind".</p>

<p>That reminds me of <a href="http://obo.genaud.net/backmatter/glossology/glossology/akalika.htm" rel="nofollow noreferrer">this definition of the word <em>akalika</em></a> (which means 'timeless'), which includes the following paragraph:</p>

<blockquote>
  <p>It is probably most useful here to go to the ultimate roots: a = no; ka = shit; li = line; ka = shit. The track of scat left by an animal. The hunter sees: This is the track a week old, this is only two days old, this is from yesterday, and here it is now, eating. That would point to the original meaning of the term to be closer to successive than to simultaneity.</p>
</blockquote>

<p>So by analogy, "born again" or "living again" might be like "pooping again": i.e. it is "again", "re-pooping", but let's be clear that they're two different poops.</p>

<p><strong>where did the concept of "rebirth" come from</strong></p>

<p>Here are a couple of articles from accesstoinsight:</p>

<ul>
<li><p><a href="http://www.accesstoinsight.org/lib/authors/thanissaro/truth_of_rebirth.html" rel="nofollow noreferrer">The Truth of Rebirth</a> starts with,</p>

<blockquote>
  <p>Rebirth has always been a central teaching in the Buddhist tradition.</p>
</blockquote>

<p>This article includes hyperlinks to the suttas.</p></li>
<li><p><a href="http://www.accesstoinsight.org/lib/authors/bodhi/bps-essay_46.html" rel="nofollow noreferrer">Does Rebirth Make Sense?</a> doesn't include specific hyperlinks but does say things like,</p>

<blockquote>
  <p>The teaching of rebirth crops up almost everywhere in the Canon, and is so closely bound to a host of other doctrines that to remove it would virtually reduce the Dhamma to tatters. Moreover, when the suttas speak about rebirth into the five realms — the hells, the animal world, the spirit realm, the human world, and the heavens — they never hint that these terms are meant symbolically. To the contrary, they even say that rebirth occurs "with the breakup of the body, after death," which clearly implies they intend the idea of rebirth to be taken quite literally.</p>
</blockquote></li>
</ul>

<p><strong>Why is it a topic of discussion?</strong></p>

<p>It's a topic of discussion because if a doctrine of "rebirth" implies there's something (perhaps a permanent self or soul) that "is reborn", then that seems to contradict other Buddhist doctrines.</p>
 111: <p>When you plant a mango seed and a mango plant comes out of it, what do you call it? Rebirth or the resurrection of the parents mango tree? Certainly not! The term 'rebirth' can be used at a conceptual level to tell a story, when we are not really focusing on whether or not there's a self or a soul. But it's inappropriate to use it when you are discussing ultimate realities. </p>

<p>ex: "Julia went to sleep last night. Julia woke up this morning". 
That's how we tell a story. But there's no 'Julia' in reality. Julia is just a concept. In reality, it is just the five aggregates which is always changing. So the Julia who woke up this morning is not the same Julia who went to sleep last night.</p>
 -1: <p>Bhikkhu Bodhi <a href="http://www.budsas.org/ebud/ebdha058.htm">writes</a>:</p>

<blockquote>
  <p>The Buddhist term for rebirth in Pali is "punabbhava" which means "again existence". Buddhism sees rebirth not as the transmigration of a conscious entity but as the repeated occurrence of the process of existence. There is a continuity, a transmission of influence, a causal connection between one life and another. But there is no soul, no permanent entity which transmigrates from one life to another.</p>
</blockquote>

<p>The word "rebirth" might be inappropriate since it implies something that borns again (and that's unlikely the meaning of what the Buddha meant). I understand this is what yutthadammo was saying. But, for better or worse, it is this english word that has been used to describe the process of "continuous becoming" in buddhism in english.</p>

<p>"With the break up of the body, after death, he/she reappears at ...", that's what we read. As ven. Bodhi said, The difficulty with this is the doctrine of anatta: if no part of our constitution is fixed, we can't talk about something that transmigrates or is reborn.</p>

<p>But at the same time, we can't say the being that died and the one that reappeared are completely unrelated. What has been said is that the "relation" (or, perhaps better, continuity) is the kamma.</p>

<blockquote>
  <p>"Student, beings are owners of kammas, heirs of kammas, they have kammas as their progenitor, kammas as their kin, kammas a as their homing place. It is kammas that differentiate beings according to inferiority and superiority."
  -- MN 135</p>
</blockquote>
