I recommend getting emulators, i have NES, SNES and GBA emulators.
The PSP games i play the most are:
Street Fighter Alpha 3 MAX and Guilty Gear XX# R, when i need my dose of fighting but i'm not home
Breath of Fire III (PSP re-release)
Ace Combat X - Skies of deception
And i also recommend:
Megamans, it's a game you can turn on, fight one or two bosses, save, and turn off. When you don't have much time to play (quick trip or something). I have nearly every megaman ever launched (that runs on a PSP, PS1, NES, Snes and GBA, of course), except for most battle networks (i already finished) and megaman & bass.
Ape Escape (Goddamn, it's so much fun. The only complaint i have is that the loading times are excruciatingly long)
And if you are into this stuff, mod your PSP to hell and back. There's so much stuff you can put into it, just like the Wii.