The PSP has a fairly unremarkable library of games, with only a few games that I'd consider "must-have"... I.E., Castlevania: The Dracula X Chronicles.
Otherwise... I went through a PSP game list and here's a few stand-outs that I think are really good, but not particularly "must-have" due to low mainstream gamer appeal, and even low appeal amongst hardcore gamers (sorry, going for more than 10 here):
Cladun: This is an RPG (there's a sequel out I think, but I haven't played it... oh and yes, "This is an RPG" is part of the game's title)
Class of Heroes
either one of the Dissidia Final Fantasy games
Disgaea (I'd suggest the DS version instead though, it's better minus a very minor graphic downgrade)
Disgaea 2
Final Fantasy IV: The Complete Collection
Gradius Collection
Half Minute Hero (there's an XBLA version of this one, just make sure to set the graphics to the retro settings in the XBLA version, the remade graphics are CRAP... the PSP version is just as solid though)
Holy Invasion Of Privacy, Badman! What Did I Do To Deserve This? (there's 3 games in this series, all of them are excellent, but hard to recommend due to the really quirky and weird gameplay)
Prinny: Can I Really Be the Hero?
Prinny 2: Dawn of Operation Panties, Dood! (both of the Prinny games are Ghosts n' Goblins style platformers with insane difficulty, but overall great fun gameplay... You get 1000 lives (total, you don't get extras) and you have to go through the game with that.... and then you realize 1000 isn't much when you lose over a hundred per level
)
Ultimate Ghosts 'n Goblins
Valkyrie Profile: Lenneth
Z.H.P. Unlosing Ranger VS. Darkdeath Evilman
Note: This is from games I've personally played, there's probably a few other good ones on this thing.