There's an interesting post chez Johnny-Dee on burden of proof (see also at Mormon Metaphysics) that got me thinking more deeply about what sort of contribution burdens of proof make to rational discussion. After some thought, I think the best way to classify them is as obligations of discourse.
Most of our work on what is rational tends to be confined to cases where there is one person thinking alone. But, of course, this is often not the case. We are often engaged in discussion and debate, and engaging in these things introduces an interesting set of complications. For instance, people don't always start with the same first principles; they don't all have the same logical ability; they don't all have the same background knowledge; and so forth. For our participation in the discussion to qualify as rational we have to be making some effort to accommodate these facts; in other words, rational discussion requires negotiation of and with the other person. One way we do that is by proposing and accepting obligations of discourse. An obligation of discourse arises when people in a discussion agree on something for the sake of argument, i.e., to see what follows. I can think of five such obligations.
(1) Basic Postulation. Example: Suppose (for the sake of argument) that I have two pennies.
(2) Technical Definition. Example: I'm using the word 'rational' (for the purposes of this argument) to mean 'having to do with logical investigation'.
(3) Request. Example: Draw a bisected angle (e.g., so I can show you how a geometrical proof works).
(4) Suspension. Example: For now let's leave aside the question of whether the problem of evil admits of precise formulation.
(5) Onus Probandi (Burden of Proof).
Burden of proof is a somewhat complicated case, so it might be worthwhile for you to bracket it a moment. (That's a case of suspension, if you didn't catch it.) Obligations of discourse are commitments for a given purpose; because of this no one ever has an obligation simpliciter. The obligation is always for a time of obligation, that is, obligations exist for as long as some condition is met (or not met, as the case may be).
For instance, suppose I'm talking with a philosophy undergrad. (That's a request .) I say to her, "Let's leave aside for the moment your conviction that there is a world outside your mind." And she agrees to that. (That's suspension .) And we discuss the matter a bit. During this entire time, we both have to conform to ; if we weren't we wouldn't be rational in our discussion. After a while I say, "OK, let's return to the way you actually experience the world." (The time of obligation for  just expired: the detour is no longer required for whatever point I was making.) (The time of obligation for  has expired. I am done with the example itself.)
The above example requires you to use your imagination a bit; this requirement, assuming you agreed to it (whether explicitly or implicitly), is an obligation of discourse. The obligation to use your imagination in this way only lasts for as long as is needed for the purposes of the discussion. Something similar occurs in the case of the suspension I proposed, to which the student agreed.
To return to burdens of proof. I would suggest that the best way to see a burden of proof is along these lines. A burden of proof is an obligation of discourse in which, given that certain things have already been proven or accepted, certain other things need to be proven for the purposes of the discussion. If this is so, we can draw out three corollaries:
(a) There is no burden of proof except in casu. There is no burden of proof in general; there are only burdens of proof in particular cases. This follows because a burden of proof can't be established except in terms to which all the parties agree. This will not always be the same, and so where the burden of proof falls will vary from discussion to discussion. One can argue similarly from the fact that an obligation of discourse is always for the purposes of the discussion, and the discussion will not always be of the same nature.
(b) A burden of proof has a time of obligation, and exists only for as long as some condition is met (or unmet, as the case may be).
(c) Since obligations of discourse only arise by acceptance (the two parties agree on something for the sake of argument), a burden of proof cannot exist where a party has not already explicitly or implicitly agreed to it. In other words, no one has a burden of proof except someone who agrees to accept it, or who is committed to the discussion in such a way that it is required. (The latter is quite common; if we find that we can't continue this particular rational discussion without accepting the burden of proof, our only other option is to end the discussion.)
Does this analysis cover everything we need to fall under the category of 'burden of proof'? I think it does if we add one more qualification. We often associate (quite rightly, I think) presumptive reasoning with burden of proof; if we can reasonably presume x, we think, the burden of proof is on those who reject x. This is often true if we remember that the presumption here is not your own, but a shared presumption. In other words, the burden of proof arises only if, given the sort of discussion you are having, you both can reasonably presume x. It is possible to presume things reasonably on your own; but burden of proof only arises in presumptive reasoning when your discussion partner is also in a position to reason the way you are reasoning. If they're not, no onus is on them, because the presumption hasn't been established for them. We cannot be asked to accept a burden of proof on the basis of something we haven't accepted.
If this analysis is at least roughly right, we should be very wary of any philosophical argument that one side or another of a dispute always has the burden of proof. It's not as if we were in a court of law, where conventions would establish beforehand many of the obligations to which the participants are committed. Further, obligations can often be reworked arbitrarily, if the participants in the discussion agree to it. Thus the people who are arguing can set the burden of proof however they wish; and there are cases in which you would happily accept the burden of proof without committing yourself to always having to accept whatever standard of proof is involved (e.g., you could just be curious about how the argument would go if the burden of proof were on you). There can be no general onus because the burden of proof ceases to be definable outside of particular cases.