I'll be the first to admit that the PSP's library blows, but there games I DO like, I like a lot. Here's my library and commentary for each game.
Castlevania: Dracula X Chronicles
Absolutely incredible game. If has the remade Rondo of Blood, the original Rondo of Blood, and Symphony of the Night all in one cheap package. If you like Castlevania, this is required playing. You might think that the modern Castlevania games cannibalize assets from Symphony, but you might not know that Symphony itself steals assets from Rondo of Blood. The Rondo games are hard as hell, but they're so freaking worth it.
Mega Man: Maverick Hunter X
If you like the MMX games, this is basically the REmake. It's very short, but graphically wonderful. The voice acting is either spot-on or horrible (as usual). Plus, once you beat the main game, you can play as Vile, which offers a completely different gameplay experience.
Mega Man Powered UP!
This is a remake of the original NES Mega Man. It offers a staggering amount of content, since you can play as all of the Robot Masters on all the difficulties...through the whole game. And then, even better, there's a level editor with tons of free downloadable content and a mission mode. The gameplay is awesome besides. Might be tough to find, but definately worth a purchase.
Metal Gear Solid: Portable Ops
If you like MGS, this is a worthy entry in the franchise. Plays differently than the console games, but in a good way. Built to be played in short bursts. Justifies the existance of Peace Walker. Do NOT buy the re-release (Portable Ops Plus). The original is far better.
Patapon
I LOVE PATAPON.
Patapon 2
I HAVE MIXED FEELINGS ABOUT PATAPON 2. It's the same game, in many ways, but in other ways, very different. The Hero offers unique gameplay, and the evolution tree is nice, but too often required, and demands additional resource mining beyond what the original game did. If pressed, I would say that the first game is better in that the experience is more streamlined. However, if you like the first one, the second one "takes it up a notch."
God of War: Chains of Olympus
In many (many) ways, this is better than God of War 2. The magic system is more streamlined, the combat is more varied, and the secondary weapon is actually useful. The story isn't as...relevant to Kratos' character, and in fact, forces an awkward inconsistency in regards to God of War 2's script (how many times has our boy escaped Hades again?). The gameplay is second to none, though, and I'm shocked that Sony isn't including it in the God of War compilation (PS3). Some reviewers whined that they didn't like how dodging was handled, but I had NO complaints.
Silent Hill: Origins
This game offers an experience that's basically similar to SH2. A lot of people didn't like it, but I my feeling is this: it's a PS2-calibur Silent Hill game. Nothing more, nothing less. Besides, it offers a unique take on the series' mythos. The final "level," though, is a little too long.
Ratchet & Clank: Size Matters
Like Origins, Size Matters is a PS2-calibur R&C game. Technically impressive, and contains all the tropes of a normal R&C outing. The hoverboard courses are a little iffy, but it's a minor complaint. The storyline is all over the place, and there's not enough Quark, even though the game leverages that big galoof early on.
LocoRoco 2
BUY THIS GAME.