Need For Speed - Carbon. It's a nice game, My cousin used to play it all
time. I tried it also and I recommend it to you also if you like racing games.
Valkyrie Profile Lenneth and Jeanne D Arc are really good rpgs on it. Final Fantasy Tactics is coming out soon. Disgaea is as well. As you can see I only buy rpgs for it.
Wipeout was a good racing game, one of the launch titles for the PSP I believe. Its been a long time since Ive bought any games for mine, Ive been largely disappointed by it on the whole.
I've played a ton of psp games and i'd have to say the psp's strong point is rpgs and puzzle games are always fun to play on handhelds. So mixing those two critieria together, the first game i'd suggest is Puzzle Quest - Challenge Of The Warlords, it's a very cool puzzle rpg game that i enjoyed a lot. It's also available for the DS, but i much prefer the PSP version.
Some recent rpgs i've liked are Jeanne D'Arc and Brave Story. Jeanne D'Arc is very similr to Final Fantasy Factics if you ever played that on the original playstation. Brave Story is more of a traditional rpg with a pretty good story.
And i think the most addictive game ever made for psp is Lumines, a simple game, but oh so fun....
That's all i can think of at the moment, I know more will come to me, as i've played a ton of psp games that i've enjoyed.
Crisis Core: Final Fantasy VII and Syphon Filter: Logan's Shadow