Patapon/Patapon 2Basically, this is a rhythm-based platformer. You tell your Pons to move, attack, and other commands by keeping the beat. There's a bit of customization involved, but it's pretty straight forward.
Taiko No Tatsujin 2May be better known as Taiko Drum Master, this is my favorite rhythm game for the PSP. The first one is pretty much exactly the same, but the songs in the second are much better. It includes some internet famous songs, such as Moskau and that Numa Numa song. Note that these are only available in Japanese, but it's pretty easy to navigate.
BeateratorMore a sequencer/mixing board than a game, I've had a lot of fun writing some stuff in this. It has a pretty high entry barrier, but once you get used to it, it's a lot of fun.
Gitaroo Man Lives!He certainly does. This game is hard. The notes fly in from all angles, and the story driven backgrounds get in the way a lot. The songs are great though, so that sort of makes up for it.
Parappa The RapperKick, punch, it's all in the mind. This game is classic. The music is just as good as you remember, and it's still pretty hard. Again, sorry for the Japanese screens. This one's in English.
DJ MAX PortableBasically Beatmania clones, there are like 10 of these for PSP. Most are in Korean, but they contain enough English to allow them to be playable.
NEXT TIME ON THIS THREAD: FIRST AND THIRD PERSON SHOOTERS