If one of the things that has you excited about PlayStation Vita includes bringing your existing PSP titles along for the ride, you may want to curb your enthusiasm a bit. While UMDs can be registered and, if available, downloaded to Vita, it will come at a price.
It doesn't look like every game will be available digitally, but the currently small list is expected to end up at around 200 titles. A dedicated application will allow players to register UMDs to a PlayStation Network account, then, should that game be available, they can download it at a discount from the PlayStation Store.
Prices, in Japan at least, appear to vary drastically. The cheaper ones start out at around ¥500 (about $6.50), but the more expensive titles can hit as high as ¥2,400 (about $31). The UMD Passport page (Japanese) has a list of currently supported titles.
According to Andriasang, PSP save files will also be transferable. Again, these are all Japanese prices and titles, so we'll have to see how this pans out in other regions. The wait for answers shouldn't be too long, though, since PS Vita is set to hit North America and Europe on February 22.