I'd probably say Socom FTB3, one of the best games I discovered on the PSP, I used to play it for hours straight, never got boring. I used to reach the highest rank within like 2 weeks without cheating.
For me it was the NHL hockey games by EA Sports. I'm a big hockey fan and love playing hockey video games so whenever I was travelling I could still play on my PSP! It was cool playing a hockey game like that on a small screen but with great graphics.
I was extremely impressed by Medal of Honor Heroes for PSP. I honestly prefer the PSPGo's version over the PSP 3000 version. The screen resolution is much better, and it feels like I'm playing MOH on PS3.
Kingdom Hearts. Though honestly I only bought it for that purpose, and haven't been able to play many games on it since. I did enjoy playing Riviera: the Promised Land until I got stuck on a level either because of a glitch or because I simply suck that bad at pressing buttons. It's likely the latter.