Sony has posted a how-to guide on downloading PSP titles to the PlayStation Vita and, along with it, a list of the 275 PSP titles and Minis that will be compatible with the Vita at launch. Obviously, it's a pretty hefty lineup, though some favorites are certainly missing, including Metal Gear Solid: Peace Walker, Valkyria Chronicles 2, Lumines and others.
That said, Sony promises more titles will be added in "the coming weeks." Head over to the US PlayStation Blog for the current list. And, before you ask, yes, of courseDragon's Lair is compatible.
Update: A couple of industry tweets reveal that some games not mentioned on the official list are already compatible with the Vita, notably Valkyria Chronicles 2 and PixelJunk Monsters Deluxe. It would appear that Sony's official list may not be entirely comprehensive. Then again, the public won't actually get its hands on the Vita for another week, so maybe there's still some tweaking going on.