I loved my PSP as well.. I had it hacked, not going to lie, mostly because of the way that some things were way more awesome with the hack. I remember having a program which gavef you the option to play music while gaming and that was awesome... ISO Shell? Something with Shell... Oh well, I loved it. If my PSP didn't break, I'd still use it now...

Here's the list of games I played on my PSP and definitely loved;
Star Wars Battlefront II - Before this I didn't really play a Star Wars game as far as I remember and I was really impressed with how much fun this one was. Eventually ended up playing this a lot..
Manhunt II - I haven't played the first one that was only on PS2, but I must say I was really amazed with this one.. It had an amazingly dark/horror style imo and I ****ing loved it! I did use a hack though, because the game was stated to be so harsh that it was censured to make it less horrible. The hack was a small thing you ran the ISO through on the PC and it removed the censure, making it awesome as f*ck.
Grand Theft Auto Liberty City Stories - My first game that I bought with my Vita. LOVED IT. Played loads on this game. Was awesome, had a lot of time on this and it's definitely worth the play!
Yu-Gi-Oh Tag Force - Can't say which version I used to play, but I loved it.. At first I was really sceptical about it because I was never that much of a fan of Yu-Gi-Oh or such, but eventually the game turned out to be fun and relaxing for me, so I played it more often than I thought.Patapon - It sounded ridiculous at first, but it was ridiculously fun though.. It was fun as hell.. Pata Pata Pata Pon! *tomtom tomtom tomtom TOM!* Oh the memories...
Tony Hawks Underground 2 Remix. - I remember this... Used to play this a lot as well, even though I'm not that big of a fan of the Tony Hawk-skate games (anymore), this game was pretty fun in my eyes. A little fast at first, but once you get used to it, you skate like hell around the levels and it was fun doing that. Had some fun aspects!

Damn.. I used to play way more than this, but I can't remember.. ;-;