i ask this every time someone posts a topic like this.

what do you like?

Well, if you don't like Jap-faggy games then you've hit jackpot.

There's dozens of great games I could recommend but I'll give you a few starters:

Third Person Games

-Syphon Filter: Dark Mirror: I always loved syphon filter but omega strain was garbage.  This game is actually better than the ps2 one and it has better production values than all the Syphon Filters.  The story mode is pretty linear and action packed, but it's got great level design, hi-tech gadgetry, and the story is pretty action-packed (although your generic action movie flare).  The online mode is completely rad and mixes Splinter Cell's stealth/trap gameplay with a bit of action and pizazz.  There's assloads of secrets too and I haven't unlocked all of them yet.

-Grand Theft Auto Liberty City Stories: It's basically Vice City except in Liberty City.  It's actually graphically better than GTA3 but the story isn't as great as San Andreas even though the origins of the characters are neat to learn.  It actually runs pretty fast with short load times and it improves on the movement and camera controls.  There's also FULL multiplayer... like, I'm not talking about tiny arenas as opposed to FULL BLOWN ENTIRE CITY AT YOUR DISPOSAL.

Death Jr: A strangely addicting game even though most reviewers didn't like it because of the camera (which is nowhere near as bad as people make it).  It's a platform hopper with a focus on MASSIVE WEAPONS and over-the-top battles.  It's actually pretty hard but really fun when you get into it.

Medievil: a remake of one of my favorite 3rd-person action/adventures, it has a bit more exploration (which might be up your alley) but tons of undead killing.  It's pretty tongue-in-cheek with awesome cutscenes and humerous dialog.

Prince of Persia: Warrior Within (the title's different but I forgot it): if you haven't played the console version then go ahead and check it out... otherwise just play the damn console version because the extra features aren't really worth it.

First Person Shooters:

-Coded Arms: This game got mixed reviews but I enjoyed it.  The controls are nowhere near as difficult as people make them out to be.  It's a mix between an RPG and first person shooter and reminds me a lot of System Shock 2 (except not as good, of course).  You run through randomly generated levels, blast aliens, collect upgrade points for your weapons (which there is quite a diverse amount) and pick up armor and attack upgrades.

Turn-Based Strategy Games:

-Generation of Chaos: a rather difficult and user-unfriendly TBS game, this one is rather rare to find but it's pretty fun once you get into it.  The battles are massive and there's tons of secrets and strategies to exploit.  It's also pretty hard and the chaotic battles turned people off but I enjoy quick play throughs.

-Field Commander: This is the king of handheld TBS games (seriously).  It's incredibly deep, features about 50+ units with their own customizations (making about 200 unique units all together), has a full blown mission + map editor (there are quite a few great ones available for download), and the multiplayer modes are a blast (you can pass the psp around, play one on one online or ad hoc, or go toe to toe with 4 other players which become rather heated).  A recommend for strategy enthusiasts.

Arcadey Games:

-Lumines: one of my favorite tetrist clones.  The gameplay is real simple but incredibly addicting.  Really, you won't put this down for a while.  I recommend this as a first buy just because it'll last you a while.

-Megaman Powered Up: I hate the newer mega man's but this remake is awesome.  The new graphics are pretty good and the new mode where you can play as the bosses adds new challenges.  The level maker is also great and there are some excellent user made maps available.

-Gradius Collection: the best collection of gradius games available.  Gradius 1-4 plus Gaiden.  It would have been nice to see Gradius V and the Lifeforce spinoffs but you can't expect everything.

-Darkstalkers: A combination of capcom's 3 arcade Darkstalkers games.  One of their better fighting game compilations.

-Street Fighter Alpha 3 Max: a jam packed upgrade of SFA3 for the arcade.  A must for street fighter fans (and has online battling mode).

-Capcom Collections: A collection of 20 or so Capcom games including Street Fighter II and Stryder among others.

-LocoRoco: a rather cute puzzle game with cartoony graphics and sacharine sweet gameplay.  It's actually rather fun but the anime-tastic look might turn you off a bit.

Racing Games:

-Burnout Legends: an all original burnout game that captures the gameplay of the console versions without losing too much detail.  Very addicting.

-Need For Speed Underground: the same as the console version but with new features.

-Wipeout Pure: one of the better and more addicting racers on the PSP.

RPG's

-PoPoLoCrois: I honestly can't recommend you this because it's quite a generic "by-the-numbers" rpg but it's story and characters touched me on a personal level so I suggest checking reviews before buying it.

-Valkyrie Profile Lenneth: one of the better ps1 rpg's, this got a facelift on the PSP with a new translation and voice cast.  It's a sidescrolling rpg with fast gameplay and puzzles and it's one of enix's best.

Hopet his helped.  As far as emulation goes, as long as you have a 2.6 psp or lower, you can downgrade to a 1.5 to be able to use homebrew.  It's a long process so I'll tell you about it if you manage to snag a 2.6 or lower PSP.

I just picked up Syphon Filter Logan's Shadow and Monster Hunter Freedom 2 and both are pretty good. Is there an online multiplayer mode for monster hunter?