AllKaiserNoBad

I never see Dead Head Fred mentioned in discussions like this, but it's probably the PSP game I've played through the most. The atmosphere is creepy and engaging and the range of combat/platforming/mini games/collectible hunting is great. It's got a decent plot with some great dark comedy moments. If you like horror tropes and beat 'em up style combat, I'd recommend checking it out!

Also Loco Roco, Daxter and Patapon, but they've been mentioned a fair bit already!

Pretty much anything from the first Ratchet and Clank game - Metropolis, Gemlik Base and Gaspar are some of my favourites