You probably know by now that the Vita is missing a UMD drive so it won't play physical media PSP games. It will, however, play PSP games downloaded from the PSN Store.
Not all PSP games will work at launch, though. Sony released a list of PSP games and Minis that will be compatible at launch (which you can read here), noting that more will be added "in the coming weeks." Most of the big names are there, such as Patapon 2, though you might be disappointed to find a few notable games, like Metal Gear Solid Peace Walker, are currently missing.
There are 275 items on the list, but it sounds like a few games that already work on Vita are actually missing. Some industry types are tweeting that games like Valkyria Chronicles II and PixelJunk Monsters Deluxe work, despite not being on the list. Sounds like it might be worth a shot to try any PSP games you happen to have laying around your account as soon as you buy a Vita.
