I've had my PSP for about a year now and am so glad I got it.
FF Tactics is a definite must-have. Not only is it ported from the PS1, there's a LOT of new goodies added. (Including the Dark Knight class) All the dialogue in the game has been redone, it sounds very epic.
EDIT: Forgot to add that every cutscene in the PS1 version was done with in-game scenes... In the PSP version, they have some very nice animations with great voice acting.
FF Crisis Core was a good choice to get. Had one of the best game endings of 2008, in my opinion. I could not put it down when I got it.
The original FF1/2 are also good pick-ups.
I've also picked up the Castlevania for it (Two Castlevania games, one that was only released in Japan for the first nintendo systems) which is a great game.
I have a Warhammer 40k Squad based combat game. Pretty damn fun.
I've got a ton of others, but my girlfriend has a DS, so we switched for a month. She has my PSP with all my games, and I have her DS with all hers.
The DS is a big pile of crap. Some of these games are just N64 ports, but you're lacking an analog stick (which the PSP has) I've gotten so many bad hand cramps from just playing Mario64DS because you use the d-pad instead of an analog stick to move around. You CAN use the touchpad, but that requires a hand to hold the DS, and a hand to use the stylus.. So your jump/punch/run buttons cannot be pushed. A lot of the DS games feel really... clunky.. I dunno, it's hard to explain. Things just feel a lot smoother and more comfortable when playing the PSP as opposed to the DS.