The appeal to ignorance consists of an argument in which the lack of evidence against a claim is taken as sufficient warrant to believe the claim in question. In effect, this is an argument in which absence of evidence is taken as evidence of absence. This is commonly regarded as a fallacy.
Burden of proof: The appeal to ignorance is complicated by circumstances in which one might reasonably argue that one side of a given debate carries a greater burden of proof than another. This is certainly true in criminal law wherein (at least in the United States) one is presumed innocent until proven guilty beyond reasonable doubt. This is also a common theme in debates over the existence of God (although its usefulness in this context is far less decisive). It is worth noting that such contexts are usually as much a function of social convention as direct concerns over evidence and truth value. The case for accepting an appeal to ignorance as a legitimate argument is thus largely built on the practical consequences of the position to be taken. Still, insofar as a burden of proof can be used to generate an argument to the effect that absence of evidence in support of one conclusion is sufficient evidence to draw its opposite is indeed an appeal to ignorance. So, the possibility that such arguments might in some contexts be compelling is at least a little problematic.
Micro-managing the Evidence: I run into a particular variation of this fallacy often enough to want to identify it as a common sub-type; I’ll call it “micro-managing the evidence.” This consists of an argument in which a given speaker demands that evidence for a given proposition must take a specific form, in effect, pre-emptively dismissing all other forms of evidence in favor of the position. This can be done either in the absence of any evidence at all or even in the face of evidence that doesn’t meet the form demanded by the author of the argument. In effect, this is an argument precluding the relevance of evidence which doesn’t meet the specific standard insisted upon by its author.
Of course , there may be good reasons to weigh certain kinds of evidence more than others, and social institutions may require that evidence take a certain form as a matter of convention, but absent such constraints, the demand that evidence take a certain form serves effectively (and often quite arbitrarily) to pre-empt other considerations. This is one more way of turning a lack of evidence into evidence of a lack, so to speak, and so it seems reasonable to consider it a variety of the appeal to ignorance.