Checking out that dental stats website will give you a good idea about which schools accept a high number of out-of-staters, but remember numbers aren't everything. For example: UMKC accepts about 25% out-of-state students, but almost all of them are from Kansas. Most schools that accept out-of-state students favor students for surrounding or boardering states. Just something else to think about. Bottom line is, find a school that takes lots of out of staters and make a 2 minute phone call to the admissions office and ask what YOUR chances are applying from YOUR state. Just my thoughts.
SUNY Stony, I think, from now on... they've had a bad track record (0-1 per year) but they said that this year (app cycle 2005) they'll accept 10 non-residents, so it looks like they're changing their policy.
Being from a state without a dental school I too had this question.
I would say state schools that accept a good number of out of staters are:
VCU, Maryland, UNLV, Michigan, Indiana, Ohio State, Iowa, Temple(if you count that as a state school), Louisville. I'm sure that there are others but that is a pretty good list.
You might want to check out the residency policies for these schools. Reall, if you can't get residency during the 4 years I would go to a private school.