I've talked before about how I hope all my lovely UMD-based PSP games will somehow work on the PlayStation Vita. Sony has not said much about how they would offer up support since the product announcement, but a new blurb in a PlayStation Vita FAQ gives me hope.
Q: I have UMD games but do I need to buy them again from PlayStation Store to play the same game on PS Vita?
A: We will consider every possibility for support on bought UMD games but we have nothing to comment at this point in time.
That's far from confirmation, but it does at least sound positive. The FAQ also states that they have no plans to bring any kind of UMD reader out for the device. Sony says that they'll continue the push to get UMD games released on their new game medium. Stay tuned and keep your fingers crossed.