I loved the PSP and DS. Both of them were fantastic and the best thing was they offered totally different games from each other. What a based time for games that was. I remember hacking the PSPs of all my younger siblings so they could play the games they wanted to play. I would buy games and then rip them myself and then put them on memory sticks for my siblings. I did the same with the DS and R4 cards which I got for all my siblings. I think off the top of my head PSP games that jump to mind are:
Crisis Core
Metal Gear Solid Portable Ops and Peace Walker and Acid
GTA Liberty City Stories and Vice City Stories
Daxter
Dissidia Final Fantasy
Jeanne d'Arc
God of War: Chains of Olympus
Tekken 5
Loco Roco
Patapon
Ratchet & Clank: Size Matters
Half Minute Hero