I had a PSP before but I sold it awhile back because I wasn't using it. I got a fantastic deal on a used PSP yesterday though, so I couldn't pass it up. Basically I got an almost mint condition PSP-1000(I couldn't believe the shape it was in), along with Assassin's Creed: Bloodlines, Madden NFL 10 and Patapon and a nifty carrying case for $60. I'm loving Madden and Patapon so far. Assassin's Creed puts the double ass back in assassin unfortunately. It's not only a step back from ACII, it's a step back from the original. I'll look into trading it in.

I want to pick up a few games for it. Don't recommend me the following games, as I've already owned them: MGS: Portable Ops, Burnout Legends, Silent Hill Origins, Daxter, Disgaea, FF Tactics, Wipeout Pure, Syphon Filter(I can't remember which one), God of War, and Crush.

There's a few kinds of games I want:

1. I want a fighting game. I like 2D fighters a lot. I'm not a big fan of 3D fighters unless it's wrestling, boxing or MMA based. Please don't recommend me Tekken or I'll kill you.

2. I want something in depth and lengthy. Maybe a sports game with a good franchise mode, a good simulation game, or an RPG with a lot of micromanagement(like Disgaea).

3. Something very light and quirky that can be saved frequently in case I want to go off and do something else.

Take into consideration loading times. PSP games are notorious for them, and I'd like to avoid owning the games that stretch on for 30 seconds every time you enter a new room or menu. Also I don't care when the game came out, so you can recommend anything from the early days to now. It makes no difference.

A few games i have my eye on that I'd like some feedback on:

LocoRoco
NCAA Football 10
The Prinny game
Need for Speed: Most Wanted
Motorstorm: Arctic Edge 

For an RPG, Crisis Core is pretty great, my favourite game on PSP, though it did only take me about 19 hours....{though the lack of jRPGs in your collection thinks this may not be perfect for you} Patapon 2 is also very very good, and if you loved the first, you should try and pick it up. I think games are region free, so if you don't want the PSN version you can probably import it

You may also want to consider some of the PSN classics because they are pretty cheap, and do involve FF VII and VIII.

Motorstorm Arctic Edge is basically just Motorstorm on the PSP, it is what you would expect and good fun.

Something quirky is Pursuit Force Extreme Justice, the main mechanic being jumping between cars. It is a really fun game, though it does have its low points with the on foot sections

Kenka Bancho might fit the bill. It's sort of like Yakuza Jr. meets all those Fire Pro Wrestling games. You get to dress up your hoodlum and customize his moveset and then wander around Kyoto getting into fights with other hoodlums. Fun!

Here's a review by a dude who rules a lot:

Of the games you listed, LocoRoco is the only one I own. It's stunning in an artistic sense, but I don't dig the gameplay so much. The mechanics are strangely unengaging to me. I still find myself playing it for the sights and sounds, though.

Final Fantasy VII Crisis Core and Disgaea 2! Also, you should get the Prinny game, one of the funnest games I've played on the Playstation Portable!

Guilty Gear XX Accent Core Plus is a good 2D fighter. I see you have Dust Strikers for the DS, not sure how different that is/whether you'd want another GG iteration.

Prinny is a great albeit short game. It's pretty nice for pick and play. Maybe Disgaea 2 will do for the tactics since you liked the first (assuming that's what you had), although it's admitedly the weakest of the three.

The new Lunar game comes out soon, It should be a good fix for your RPG needs!

GTA: Liberty City Stories
GTA: Vice City Stories
Midnight Club 3: DUB Edition
Ratchet and Clank: SM
Phantasy Star Portable
Monster Hunter: FU
Gran Turismo (it's a great game)
Dissidia: Final Fantasy (it's 3D fighting but it's awesome)

If you have a friend or two you should give a try to Monster Hunter.It's huge in length,action packed and hard(in a good way).It doesn't have a lot of micromanagements as it is quite basic and straightforward but that's because it's a more action-oriented with rpg elements game than a real RPG.Last if you have a ps3 you can play online. ;)

I don't have a friend or two. However Monster Hunter still interests me. Which is the best one to look into?

A fantastic addition to an awesome franchise. Patapon 2 offers a new story mode, more unit types + level up system, a hero Patapon to lead your army, different bosses, different weapons, more minigames for getting item components, and just about anything you loved in the first game X10.

also LocoRoco: Midnight Carnival

All of the games listed above are highly unique platforming games. Some of my favorite games period, each one offers the player a different experience with great level design, collectible items scattered across the levels + secret areas in each level, and a highly amusing storyline. I would suggest you check this series out.

Half Minute Hero, you want a great game you can pick up and put down quickly? Well, please watch this video

I love it! I would check it out!!! ^_^

You said you were interested in this title? It's great! A funny story, good platforming and level design, nice challenge level, great bossfights, it's all around a great title. I would give it a go or at least check it out further. Plus, I'm sure you can secure this game for under $20 just like pretty much all these games!

Also Pixeljunk Monsters Deluxe! It takes the Ps3 fantastic game, Pixeljunk Monsters and add so much more! Here, take this video

This is a short list, hope it helped!