user113: Orthodoxy in Christianity is the holding to the oldest beliefs.  It is of course impossible for the religion not to evolve at all as new questions and there answer have to addressed. The "Orthodox" version is often considered to be the least evolved sect of a religion.  Does the concept of Orthodox apply in Buddhism? 

user-1: James Jenkins, those interested, 
it's a sign of the Dhamma-Vinaya, the Buddhas teachings, to be very orthodox and it's because his good following disciples stayed by what was taught by him as much as they could remember and recollect, that his "(re)-legion" could be brought till this days and is still alive to be used.
What ever "unorthodox" approaches, often simply copies, are traced, can, for the most, be seen as not of what the Buddha taught and advice, yet he gave a lot of advice to proof such seriously without either to reject or take on it at first place, if unusual practices and teachings are approached and one of this sets of tools to prove is called Great Standards, also found under the link above, among other tools to verify the "orthodoxy" and validity of sayings and usual, mostly alien to the Theras (Elders of the monastic community).
While the practice of lay-followers may change over time, which is surely often also followed by certain disciples and particular communities of monks, of course always lead by certain improper desires, the ways the so called "Savaka Sangha" (community of good following disciples of Bhikkhus), the way of the Noble Ones didn't really changed, is still, even if hard to trace and find, alive although decaying naturally. Once the (Re)-legion goes astray, there is no much benefit for it, better it could not contribute much for benefit in the world, which is also a reason why this (re)legion would not adapt common desires simply for the sake of existing on or for maintaining ways of merely for the use of just livelihood and entertaining. 
Once the "Religion" is or appears no more orthodox it will be no more maintaining a monastic Sangha which is a huge and unexcelled field of merits.
The essay and collection of That the True Dhamma Might Last a Long Time: Readings Selected by King Asoka may give also some impressions of the Dhamma-Vinayas ("Budddhisms") orthodoxy, which is actually, although claimed otherwise, even since the Mahaparinibbana of the Buddha, most compassionate this upholding of orthodoxy.

Now at that time, one Subhadda, who had renounced only in his old age, was seated in the assembly. And he addressed the bhikkhus, saying: "Enough, friends! Do not grieve, do not lament! We are well rid of that great ascetic. Too long, friends, have we been oppressed by his saying: 'This is fitting for you; that is not fitting for you.' Now we shall be able to do as we wish, and what we do not wish, that we shall not do."
But the Venerable Maha Kassapa addressed the bhikkhus, saying: "Enough friends! Do not grieve, do not lament! For has not the Blessed One declared that with all that is dear and beloved there must be change, separation, and severance? Of that which is born, come into being, compounded, and subject to decay, how can one say: 'May it not come to dissolution!'?"

What ever one nourishes, inwardly, outwardly, that will grow and resist for the individual as well as the opposite. It's seldom, very seldom that one gives into Upasnissaya of the Noble Ones, but having done and do so, one does not need to worry to come not near and sooner or later access the Orthodoxy that leads not only to heavens but to final release form all stress and suffering. Good and bad choices are individual ones, yours, which no one could force.
James Jenkins stated in his question: "It is of course impossible for the religion not to evolve at all as new questions and there answer have to addressed.", actually it is, was done by the Sublime Buddha, to release a timeless path and teaching, ever-trace and usable for those ready to be tamed.
(Note that this is not given for trade, exchange, stacks or entertainments binding one in this world but as means for an exit from this wheel)

user471: Orthodox Buddhism would be what we call Pre-sectarian Buddhism, which does not exist any more, as a tradition or school or sect. Pre-sectarian Buddhism split into the Mahasamgika school and the Sthavira school.
The modern Theravada tradition, is probably the closest modern school to Pre-sectarian Buddhism, in terms of its doctrines. Theravada is based on the Sri Lankan Mahavihara school, which descended from the South Indian Tamraparniya branch of the Vibhajyavada school, which descended from the Sthavira school.
In this blog post, Ven. Sujato wrote:

The term sthavira (mean­ing ‘el­der’) is the Sanskrit ver­sion of the
term bet­ter known to­day in its Pali ver­sion thera, as in Theravāda,
the ‘Teaching of the Elders’. The orig­i­nal Sthaviras, how­ever, are
by no means iden­ti­cal with the mod­ern school called Theravāda.
Rather, the Sthaviras are the an­ces­tor of a group of re­lated
schools, one of which is the Theravāda.

To me, the most orthodox teachings of Buddhism are found in the Theravada Sutta Pitaka and the Mahayana Agamas, which are essentially the same thing.
Personally, I don't consider the Theravada Abhidhamma and the later Mahayana Sutras (like the Lotus Sutra or Heart Sutra) to be orthodox.

user145: There is no Orthodox Buddhism, there is Traditional Buddhism. Most modern traditional branches of Buddhism with monkery, root in some or other ancient school. Theravada is not more Orthodox or ancient than most other traditional schools.

user28: Well, Theravada is often argued to hew most closely to the original teachings of the Buddha. See, e.g. "Two Main Schools of Buddhism" for a very brief overview of this. 
As I understand it, this has much to do with the fact that Theravada is the oldest of the extant Buddhist schools of thought, predating Mahayana by a few centuries. Theravada practice is also more localized to geographic regions nearer the birthplace of Buddhism (that is, Sri Lanka and Southeast Asia), and never strayed far from it; this is thought to have contributed to the "orthodoxy" of the school - it mixed less with other intellectual and spiritual traditions.
Additionally, Theravada Buddhists draw primarily on the Pali Canon (the Tripitaka), whereas Mahayana Buddhists draw primarily on Chinese sources. These Chinese sources are relatively more distant from the original teachings of the Buddha in terms of both time and language. As a byproduct of this, the Pali texts are often more "authentic".1
That said, the term "Orthodox" has no specific meaning in the context of Buddhism, i.e. there is no such school as "Orthodox Buddhism". There are only lowercase-o "orthodox schools of Buddhism", and what counts as "orthodox" will probably differ depending on who you ask. I should add that pre-sectarian Buddhism is almost definitionally the most "orthodox" school of Buddhist thought. The only problem is that, well, it doesn't exist anymore.

1 See, e.g. Rupert Gethin's The Foundations of Buddhism, p. 44: "it is likely that [it] is generally the case [...] that the traditions [the Pali recension] preserves are [...] the oldest and most authentic available to us" (elisions/etc because the original sentence was inverted)

113: <p><a href="https://en.wikipedia.org/wiki/Orthodoxy">Orthodoxy</a> in Christianity is the holding to the oldest beliefs.  It is of course impossible for the religion not to evolve at all as new questions and there answer have to addressed. The "Orthodox" version is often considered to be the least evolved sect of a religion.  Does the concept of Orthodox apply in Buddhism? </p>
 -1: <p>James Jenkins, those interested, </p>

<p>it's a sign of the <a href="http://zugangzureinsicht.org/html/lib/authors/thanissaro/bmc1/bmc1.intro_en.html#intro1" rel="nofollow noreferrer">Dhamma-Vinaya</a>, the Buddhas teachings, to be very orthodox and it's because his good following disciples stayed by what was taught by him as much as they could remember and recollect, that his "(re)-legion" could be brought till this days and is still alive to be used.</p>

<p>What ever "unorthodox" approaches, often simply copies, are traced, can, for the most, be seen as not of what the Buddha taught and advice, yet he gave a lot of advice to proof such seriously without either to reject or take on it at first place, if unusual practices and teachings are approached and one of this sets of tools to prove is called Great Standards, also found under the link above, among other tools to verify the "orthodoxy" and validity of sayings and usual, mostly alien to the Theras (Elders of the monastic community).</p>

<p>While the practice of lay-followers may change over time, which is surely often also followed by certain disciples and particular communities of monks, of course always lead by certain improper desires, the ways the so called "Savaka Sangha" (community of good following disciples of Bhikkhus), the way of the Noble Ones didn't really changed, is still, even if hard to trace and find, alive although decaying naturally. Once the (Re)-legion goes astray, there is no much benefit for it, better it could not contribute much for benefit in the world, which is also a reason why this (re)legion would not adapt common desires simply for the sake of existing on or for maintaining ways of merely for the use of just livelihood and entertaining. </p>

<p>Once the "Religion" is or appears no more orthodox it will be no more maintaining a monastic Sangha which is a huge and unexcelled field of merits.</p>

<p>The essay and collection of <a href="http://zugangzureinsicht.org/html/lib/authors/thanissaro/asoka_en.html" rel="nofollow noreferrer">That the True Dhamma Might Last a Long Time: Readings Selected by King Asoka</a> may give also some impressions of the Dhamma-Vinayas ("Budddhisms") orthodoxy, which is actually, although claimed otherwise, even since the Mahaparinibbana of the Buddha, most compassionate this upholding of orthodoxy.</p>

<blockquote>
  <p><a href="http://zugangzureinsicht.org/html/tipitaka/dn/dn.16.1-6.vaji_en.html" rel="nofollow noreferrer">Now at that time</a>, one Subhadda, who had renounced only in his old age, was seated in the assembly. And he addressed the bhikkhus, saying: "Enough, friends! Do not grieve, do not lament! We are well rid of that great ascetic. Too long, friends, have we been oppressed by his saying: 'This is fitting for you; that is not fitting for you.' Now we shall be able to do as we wish, and what we do not wish, that we shall not do."</p>
  
  <p>But the Venerable Maha Kassapa addressed the bhikkhus, saying: "Enough friends! Do not grieve, do not lament! For has not the Blessed One declared that with all that is dear and beloved there must be change, separation, and severance? Of that which is born, come into being, compounded, and subject to decay, how can one say: 'May it not come to dissolution!'?"</p>
</blockquote>

<p>What ever one nourishes, inwardly, outwardly, that will grow and resist for the individual as well as the opposite. It's seldom, very seldom that one gives into Upasnissaya of the Noble Ones, but having done and do so, one does not need to worry to come not near and sooner or later access the Orthodoxy that leads not only to heavens but to final release form all stress and suffering. Good and bad choices are individual ones, yours, which no one could force.</p>

<p>James Jenkins stated in his question: <code>"It is of course impossible for the religion not to evolve at all as new questions and there answer have to addressed."</code>, actually it is, was done by the Sublime Buddha, to release a timeless path and teaching, ever-trace and usable for those ready to be tamed.</p>

<p><em>(Note that this is not given for trade, exchange, stacks or entertainments binding one in this world but as means for an exit from this wheel)</em></p>
 471: <p>Orthodox Buddhism would be what we call <a href="https://en.m.wikipedia.org/wiki/Pre-sectarian_Buddhism" rel="nofollow noreferrer">Pre-sectarian Buddhism</a>, which does not exist any more, as a tradition or school or sect. Pre-sectarian Buddhism split into the Mahasamgika school and the Sthavira school.</p>
<p>The modern Theravada tradition, is probably the closest modern school to Pre-sectarian Buddhism, in terms of its doctrines. Theravada is based on the Sri Lankan Mahavihara school, which descended from the South Indian Tamraparniya branch of the Vibhajyavada school, which descended from the Sthavira school.</p>
<p>In <a href="http://santifm.org/santipada/2010/why-devadatta-was-no-saint/" rel="nofollow noreferrer">this blog post</a>, Ven. Sujato wrote:</p>
<blockquote>
<p>The term <em>sthavira</em> (mean­ing ‘el­der’) is the Sanskrit ver­sion of the
term bet­ter known to­day in its Pali ver­sion <em>thera</em>, as in Theravāda,
the ‘Teaching of the Elders’. The orig­i­nal Sthaviras, how­ever, are
by no means iden­ti­cal with the mod­ern school called Theravāda.
Rather, the Sthaviras are the an­ces­tor of a group of re­lated
schools, one of which is the Theravāda.</p>
</blockquote>
<p>To me, the most orthodox teachings of Buddhism are found in the Theravada Sutta Pitaka and the Mahayana Agamas, which are essentially the same thing.</p>
<p>Personally, I don't consider the Theravada Abhidhamma and the later Mahayana Sutras (like the Lotus Sutra or Heart Sutra) to be orthodox.</p>
 145: <p>There is no Orthodox Buddhism, there is <em>Traditional Buddhism</em>. Most modern <em>traditional</em> branches of Buddhism <em>with monkery</em>, root in some or other ancient school. Theravada is not more Orthodox or ancient than most other <em>traditional</em> schools.</p>
 28: <p>Well, Theravada is often argued to hew most closely to the original teachings of the Buddha. See, e.g. <a href="http://www.budsas.org/ebud/whatbudbeliev/59.htm">"Two Main Schools of Buddhism"</a> for a very brief overview of this. </p>

<p>As I understand it, this has much to do with the fact that Theravada is the oldest of the extant Buddhist schools of thought, predating Mahayana by a few centuries. Theravada practice is also more localized to geographic regions nearer the birthplace of Buddhism (that is, Sri Lanka and Southeast Asia), and never strayed far from it; this is thought to have contributed to the "orthodoxy" of the school - it mixed less with other intellectual and spiritual traditions.</p>

<p>Additionally, Theravada Buddhists draw primarily on the Pali Canon (the Tripitaka), whereas Mahayana Buddhists draw primarily on Chinese sources. These Chinese sources are relatively more distant from the original teachings of the Buddha in terms of both time and language. As a byproduct of this, the Pali texts are often more "authentic".<sup>1</sup></p>

<p>That said, the term "Orthodox" has no specific meaning in the context of Buddhism, i.e. there is no such school as "Orthodox Buddhism". There are only lowercase-o "orthodox schools of Buddhism", and what counts as "orthodox" will probably differ depending on who you ask. I should add that <a href="http://en.wikipedia.org/wiki/Pre-sectarian_Buddhism">pre-sectarian Buddhism</a> is almost definitionally the most "orthodox" school of Buddhist thought. The only problem is that, well, it doesn't exist anymore.</p>

<hr>

<p><sup>1</sup> See, e.g. Rupert Gethin's <em>The Foundations of Buddhism</em>, p. 44: "it is likely that [it] is generally the case [...] that the traditions [the Pali recension] preserves are [...] the oldest and most authentic available to us" (elisions/etc because the original sentence was inverted)</p>
