James Chastek has a nice little post on burden of proof that I think is exactly right. Burden of proof is something I think we tend to handle in far too clumsy a fashion. To handle it properly requires stepping back and considering how it actually functions.
Burdens of proof really arise because reasoning doesn't consist in merely picking out some premises and tracing out their ramifications. There is much more to it than that, and at least part of reasoning consists in discussion and debate, which are a rather more complicated thing than simply inferring from premises. Moreover, the bulk of real reasoning probably consists in this more complicated form. Most of the obvious cases in which we are laying down sequences of premises and conclusions are cases in which we deliberately set out to do so; all the natural cases are cases of reasoning that arise naturally either in discussion or debate, or else when we are, so to speak, considering two or more sides to a discussion or debate on our own, and thus guessing as to what people might say to this or that. Human reason is social by nature.
Any social case, however, requires a sort of negotiation with others. We have to get the agreement of others. And we can't just get an abstract agreement about the truth of particular claims. We have to ask the other people to do things -- follow along with this or that reasoning even if they don't immediately see the point, try something out, consider a particular case, and so forth. We can call these obligations of discourse. Again, these obligations of discourse are really negotiated; they become obligations due to the agreements of those involved. It is in this context that I think burden of proof really arises.
I have previously suggested that there are at least five types of obligation of discourse. The first four are fairly straightforward, and rise out of a fairly straightforward set of things that we may try to establish by agreement as part of the discussion:
(1) Basic Postulation. This occurs whenever we agree to consider a particular case for the sake of argument.
(2) Technical Definition. In order to be clear, precise, or accurate, we often have to use terms in specialized senses; but these specialized senses, too, need to be acceptable to others.
(3) Request. Sometimes we need to get the other person to do something; so we request that they do it. For example, to show you the proof of a geometrical claim, I may ask you to draw a bisected angle.
(4) Suspension. Sometimes there are more issues potentially on the table than can reasonably be dealt with. In such a case, in order to keep the discussion usefully focused, we have to agree to set aside something for the purposes of this particular discussion.
Every obligation of discourse is created when these argumentative moves gain agreement: by agreement, we might say, the parties involved commit themselves to something and therefore oblige themselves to act in light of that commitment. The obligation, however, is never indefinite; it is always for a limited time of obligation. That is, every obligation of discourse lasts only as long as some condition is met (or, perhaps, as long as some condition is not yet met). Even at the most minimal level, nobody is obliged to suspend discussion of a particular topic for longer than the particular discussion in which they agreed to the suspension lasts.
The burden of proof is another example of an obligation of discourse. It is a rather more complicated example, however, due, perhaps, to the fact that it was developed for a specialized area of life -- law -- and has since been extended to other areas of life by analogy. But it shares the same features: 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 this particular discussion. In particular, a burden of proof arises when the parties involved agree to a shared presumption: they both agree to presume (for the sake of this particular discussion) that something is not established unless some conditions are met.
From this it follows that burden of proof is only had in casu -- it arises within a particular case, due to agreements (tacit or otherwise), and it terminates with that case. If another case arises, the burden of proof has to be reconstituted by a new agreement. Likewise, it follows that a burden of proof cannot exist where a party has not already explicitly or implicitly agreed to it. It is clear enough that this is true in the original case, that of the court of law. Independently of any truth of that particular case, we establish courts to be run on certain procedures; these procedures have established burdens of proof that are widely considered reasonable; and by coming before the court, everyone agrees to accept these conventions for distribution of burden of proof. In areas of life that do not involve these standing conventions you can still have burdens of proof, but they must be constituted on a case-by-case basis.
Given this, we should be wary of any attempt to say that on a philosophical topic one particular position always has the burden of proof. There are no standing conventions for burden of proof in philosophy; and, in fact, philosophers often play with different kinds of burdens of proof on a particular topic, just to see what happens if you set the burden of proof in a different way. (The fact that we can agree to change the burden of proof, even on mere whim, is one of the many things that shows that burden of proof is in fact constituted by such agreements. Even where burden of proof has been created, it may be created for reasons that have nothing to do with truth, or with proof itself, since burdens of proof are reasonable or unreasonable depending on how they meet the ends of the discussion or dispute -- which may not always be truth, or at least truth alone.) Moreover, in many instances it is clear enough that the whole purpose of such claims is an obvious attempt to make things easier on oneself; while you occasionally find them, overwhelmingly people expend their energy trying to prove that other people have the burden of proof. And this is not surprising; if you can get everyone else to shoulder the burden of proof, that puts you at an immediate advantage in the argument, since everyone else has to argue and you don't have to do anything but check to see whether they have proven what they have agreed to prove. Thus people try to distribute the burden of proof to other people regardless of whether such a distribution of burdens is conducive to truth, or particularly reasonable given the circumstances.
Note incidentally, that it does not follow from any of this that there are no reasonable arguments about burdens of proof. No one ever automatically has the burden of proof on anything; burden of proof is not a logical feature of one's position or arguments but a convenience and courtesy whose precise details must be worked out by everyone involved. In many cases it will be convenient for everyone to agree on some set of things that must be done to resolve the dispute, and one can reasonably argue about whether this or that set of things is the most reasonable set to choose. In other words, not every distribution of the burden of proof is equally conducive to the ends of discussion (truth, protecting the innocent, action, or whatever), and we can reasonably agree that there needs to be a burden of proof but disagree about who should have it. (On rare occasions it might even be the case that one person should clearly have the burden of proof, given the ends of discussion and the shared commitments of the participants in the discussion.) In every case involving burden of proof, it arises because participants have come to some sort of agreement, either in the case itself, or as a matter of convention, that the burden of proof should be given to someone because it makes sense for them to have it, given what the people in the discussion or dispute are doing. We can also, of course, not worry about burdens of proof at all. Outside of actual debates and heated disputes we rarely do, in fact. The paradigm case for burden of proof, that found in court of law, is a case in which we have burden of proof for practical reasons related to how courts have to work; this is a key asymmetry between arguments in court and rational discussion generally.