Spyro games work surprisingly well with the analog nub. I booted up Spyro 3 and I was blown away at how well it controlled. I was just as good as it as I was when I beat the shit out of that game so many years ago. Unfortunately, Crash Bandicoot doesn't work all that well (the analog stick and D-Pad are just too wonky).
Final Fantasy VII and IX work fine (I'll assume VIII does too). Most standard RPG outings work fine, actually (although some of the Final Fantasy anthology games run terribly, there's just technical issues and stuff).
If you want to count remakes, there's tons of pretty solid ones. The first and second Final Fantasy got good remakes (they're still a bit dated but the remakes make them playable), the fourth Final Fantasy did as well (absolutely amazing on the PSP), and there's also Valkyrie Profile: Lenneth (pretty fun RPG although the voice acting is kinda shitty and the intro is like a solid hour of straight dialogue with I think three battles).
Chrono Cross is like one of the best PSX (and RPG) games ever made and it runs fine on the PSP if you fiddle with it (correct popsloader version and Game ID), although there's a bit of slowdown when entering a battle. But it's fucking Chrono Cross so who gives a shit.
Also, Castlevania: Symphony of the Night is just like the best PSX game on the PSP. It just runs perfectly and the controls are awesome. Also probably the best 2D game ever made. Einhander also works pretty well in regards to controls.