[Update: Evidently, Sony's press release states that you need to own the UMD first to get a free transfer.]
Over in Japan, the PSP-to-Vita service is a bit different. They have a program called "UMD Passport," where you can get discounted version of PSP games for Vita. According to Siliconera it's going to get a lot better soon though starting September 17th.
From that date until the end of the year, all PlayStation Plus subscribers will be able to play the entire UMD Passport collection for free. That includes 370 total games. Wow! If only Sony had something similar overseas, or Nintendo had that program for the Virtual Console.