The must have games for the psp in my opinion would be (Keep in mind to the category as some players dislike certain types of games).
Action/Adventure
Kingdom Hearts: Birth by Sleep
Jak and Daxter the lost frontier (also involves a bit of flying)
Final Fantasy Crisis Core (also kind of RPGish)
God of War: Chains of Olympus
Assassin's Creed Blood lines (looks promising)
GTA were also fun (forgot about those)
(Maybe Prince of persia I was a hunch fan of the ps2 series but I don't know how well they ported them.)
Also Metal Gear Solid either PO or Peace Walker
Patapon 1 or 2 (action/rhythm side scroller) they're very similar
Crush if you enjoy puzzle games
Final fantasy tactics for tactical RPG
I neglected music games as well as racing.
If you like racing Ridge racer.
for music rockband could work.
Those are in my opinion the must haves I may be missing a few. I'll amend it if that's the case.
nighthawk260
this list. and Resistance: Retribution 
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