If you're into RPGs and Tactical games now, get FF Tactics and Valkyrie Profile.
Since you're a DBZ fan, I think they made two fighting games for it, with the second possibly being a what-if featuring Future Trunks dealing with Majin Buu in his world.
Don't quote me on that, but if it's true, you gotta admit, it'll be something to see how he deals with him.
I've only got one game so far, which is Monster Kingdom: Jewel Summoner. I'm a fan of the Shin Megami series and this was a new series started by the game creator.
I dunno when I'll get my next PSP game though.
Anyhoo, I talked to Naruto and he's recommended Valkyrie Profile, Dungeon Siege, Jeanne D'arc, Guilty Gear Judgment, Tekken, and Wipeout for certain genres.
It depends on what you're into though. The first three listed are RPGs or Tactics, the next two are fighting games, and the last is a racing one.