There were some games that had a feature called game sharing. This let you send a smaller version of the game, essentially a demo, to another PSP over wifi, and this let you at least try the experience without owning the game. Burnout Legends definitely did this, but I also remember it on some NFS and sports titles. I just found a list of games that did this.[0] Also, there were some good shooters as well, like Medal of Honor or Battlefront, with pretty nice maps, especially for a handheld. And for racing games, Gran Turismo was incredible with almost all GT5 tracks and 900+ cars present.

[0] https://www.lifewire.com/psp-games-with-gameshare-2792549