There are actually quite a few games that I really enjoyed that have a PSP version for them. When you play things as a kid, it is really hard to tell if you were amazed by a sub-par game or it was amazing so I can only go off of what I felt then. There was a game called Daxter which was pretty good just with the storyline and all the various elements to the game; the graphics weren't all that though. Another one was Final Fantasy Dissidia; that one had a great storyline and graphics for the time. There is also a series called Dynasty Warriors which maybe doesn't have the best graphics or storyline, but the gameplay was superb. Being able to get stronger and upgrade your character is a simple but enjoyable aspect of games and I feel that Dynasty Warriors allows you to truly feel the changes that happen with your character as you upgrade them and get stronger. I almost forgot, Metal Gear Solid was AWESOME. It is a pretty popular game so there isn't really a need to elaborate on the game itself. Another great multiplayer game was the Ghost Recon series which is similar to metal gear solid but with friends.