There's some interesting discussion going on around the web as to whether some form of naturalism - philosophical or methodological - is presupposed by science. Tom Clark has a useful post here, and there some good exchanges on Richard Dawkins' site. I haven't yet had a chance to absorb this article by Yon Fishman, except for its abstract, but I promise to look for the full text.
It appears to me that Fishman may well be correct in his criticism of the reasoning in the Dover decision, though that would not imply that the Dover judge reached the wrong result, since the ultimate issue is not whether a body of beliefs with a supernatural element could be science but simply whether, in all the current circumstances, the teaching of Intelligent Design in state schools in the US is forbidden by the First Amendment. I think there's ample reason to believe that it is. In any event, even if it would be possible in principle for intelligent design to be genuine science - notwithstanding its supernatural element - there is no basis to believe that it is genuine science in its current form. The main reasoning in the Dover decision does not seem to be marred by anything along the way that is not strictly correct (although there is surely room for further discussion about how the reasoning should best be recast).
Here is the best summary I can give as to why even methodological naturalism is not strictly required for the practice of science.
First, many scientists have historically proposed hypotheses that don't conform in any strict sense to a requirement of methodological naturalism: hypotheses that seem to require supernatural interventions from time to time or one-off. Some early theories of reproduction seem like this, as do theories that explain the geological strata in terms of Noah's flood, and we could probably think of other examples. I'd rather not say they were doing something other than science. Such an approach to science has not been fruitful, but it seems to me that it was a kind of science as science has been understood historically.
Second, science can indeed examine some of these hypotheses to see whether the evidence favours them, which is just as well. After all, we'd like to know whether these theories are actually likely to be correct without just ruling them out a priori.
As a massive understatement, the 19th-century Noah's-flood theory of geological strata and fossils seems untenable. Even without our modern knowledge of how geology actually works, we can see how it can't do the job it was supposed to do, and it's an embarrassment to those Young Earth Creationists who still rely on it. (I owe the thrust of the following to Philip Kitcher, though I'm giving a brief and garbled version for which Kitcher is not at all responsible.)
The Noah's-flood theory does give some sort of explanation as to why fish first occur lower in the geological strata than flying animals such as birds, but it should predict that flightless birds will appear lower in the strata than ordinary birds. Likewise, bats should be at the top of the strata, higher than primates. (This is very simplified, why should animals that like water, like fish, die in the flood before birds? The animals at the bottom should be whatever are most vulnerable to being killed by flooding. Flying birds should, however, be among the last to go, as they can easily get to higher ground and even fly above the waters until they eventually fall from starvation or exhaustion ... so, you get the idea. The point is that the theory fails to match the detail of fossils and strata, and became hopelessly impossible to hold onto even in the 19th century.)
Similarly, we can examine the evidence for such things as the power of intercessory prayer (as Tom Clark's post indicates), the efficacy of claimed supernatural powers, and so on. As long as those theories give systematic accounts of how things should happen, it's possible in principle to test whether the evidence favours them.
I'd say that the use of supernatural explanations has not been fruitful, and that these explanations should not be preferred as they are often ad hoc, fail the test of consilience, and so on, but they are not rejected a priori. They can be science, but so far they have been shown to be very bad science. Intelligent Design is arguably not science at all, because it is not able to postulate any system by which its seemingly supernatural "intelligence" works, but in principle there could be a version of ID that is more scientific. The trouble is that no one has any clue what it would be like - the idea made some sense in the 19th century, but it now appears to be a dead end, and we have plenty of evidence that efforts to promote ID are motivated by religious piety rather than by genuine efforts to augment biological science with new kinds of systematic explanation.
One kind of theory that science can never test in any systematic way is the self-insulating "deceptive creator" theory: e.g., the omphalos theory that God created the Earth 6000 years ago, complete with all the signs - such as fossils - of a much longer history. However, scientists, like anyone else, are entitled to dismiss this kind of theory as implausible and ad hoc rather than ruling it out merely because it posits something supernatural.
I should add that if we accept that all the above is correct, only to say that anything science can postulate is "natural" by definition, we are making methodological naturalism trivially true, in which case it gives no methodological guidance. We want to be able to test, rather than rule out a priori, a whole lot of claims about interventions by deities, the actions of individuals with anomalous psychic or magical powers, and so on. If these are supernatural, then testing the evidence for supernatural hypotheses is part of science. If they are considered part of "the natural", should they turn out to be real entities, forces, and so on, then methodological naturalism has no content. Indeed, once we define "the natural" in such a way, any kind of naturalism is devoid of substantive content - philosophical naturalism would boil down to something like, "The only kinds of things that exist are the ones that exist." Naturalism may end up having some irreducible vagueness to it, but it must have some content.
However you analyse it, neither philosophical naturalism nor methodological naturalism appears to be necessary for science. Philosophical naturalism is a meta-inference about what sorts of things are likely to exist - based on all the well-corroborated scientific inferences to hand - and it should be thought of as a philosophical theory rather than as part of science. It's a highly plausible theory - one that I subscribe to - even if difficult to state with total precision. Methodological naturalism is more a summary of the (again plausible) idea that supernatural hypotheses tend to be bad science. That may create a mild, practical presumption against using supernatural hypotheses, but it doesn't rule them out of all contention.