good psp games that suck:
jeanne d'arc: it's been mentioned before, but, the thing you got to know about this game is a) the boss fight is reeeeaaaallly hard and a pain in the ass - but that's good! and b) the french accent of all the english dub cast is hilarious - it kills any suspense, but it's so much comedy! The rest sucks imo, gameplay is cool for all it's worth, but fighting against orcs n' Trolls n' shit alongside elves is not what I had in mind after having picked it up. Still entertaining though.
300 - March to glory: It's fun, it's bloody, it's good - okay looking, it can get on your nerves so bad you beginn hating rhinos. And I had some crazy love for my rhinos...
Chillie Con Carnage - think old gta, with little gta in it, but a lot more comedy and action and shoot outs, and crazy shit. A diamond in the rough of fun.
Innocent Life: A futuristic harvest moon: picture this: you are a robot, devoid of emotions and dumb, but eager to learn and everybody loves you! it's so unrealistic, it's gorgeous! Don't know about the fun in planting stuff yet though...
Parappa the Rapper: It's funny, it's fresh, it's "cool", it's rap and it's hard as hell, I can't get past the third song....the third >_>
Pirates!: Pirates - nuff said.
WTF: The name, really, it's all just the name.
good psp games that are also good:
Crazy Taxi Fare Wars: Crazy Taxi 1+2+Multiplayer = win
Death Jr 1+2: coolest jump n' run on the psp
Flatout - Head On: Great graphics and awesome racing game
Metal Slug Anthology: It's Metal Slug, all of it! Nope, I won't state the obvious.
CRASH, Exit 1/2, N+, Space Invaders Extreme: all nice snack bite games for on the go, with the latter being a bit trippy though.
Worms Open Warfare 1/2: Worms is great, even better on the go.
Tokobot: cool platformer. As a jr archeologist you discover robots - tokobots - from an ancient civilisation that are real nice and sweet and the hold hands with each other....so you can use dem to smash stuff and get to far away places.
Warhammer 40k: Squad Command: the best for last, this game got me into turn based strategy using action points, which I used to despise. But Squad Command handels it so well, adding a layer of depth that is neither complex nor superficial. The setting is awesome anyway, playing the space marines you get to equip your units with unlockable weaponsets and the surroundings are completely destroyable. There are a few faults though, story is kind of thin - even though it does give you the feeling of waging real war(=a great ammount of small but tactically important battles) it feels a lot like waging a meaningless war...also you never get to choose which units you send out on the mission, you get them assigned. And theres only chaos and space marines, both with 3 different legions to add a bit of variety. Multiplayer is cool though.
Some general suggestions...
...if you like Strategie-RPGs: Final Fantasy Tactics - The War of the Lion/FF Tactics (PSX), Disgaea - Afternoon of Darkness, Riviera - The Promised Land (just gotta luv angels vs demons ~)
...if you like RPGs: Breath of Fire 3, Final Fantasy Anniversary I + II, Popolocrois, Tales of Eternia, Tales of the World - Radiant Mythologie, Valkyrie Profile: Lenneth (awesome art design), Silverfall
...if you like to run/drive/fly around town, blowing stuff up, bein a gangsta: GTA - Vice City Stories and Liberty City Stories, Scarface - Money Power Respect, The Godfather: Mob Wars, The Warriors, Gangs of London
...if you like PSX: Diablo (the best portable experience ever

), Duke Nukem - Time to Kill, Parasite Eve, Final Fantasy incarnations and Vagrant Story. Oh, and Cowboy Bebop if you know you're japanese. I do not. Count me sad.