Patapon is a unique rhythm based game where you control little soldiers to fight for you. Basically you're their god and you can make them march forward, attack, retreat, or defend, based on the beat that you give them. You make them fight various missions for you and you can outfit them with weapons and armor you find.
Yeah, space invaders extreme is really good to if you liked space invaders. They've blended music and classic space invaders gameplay in to an entertaining game that expands on teh basic concept with powerups and whatnot.
If you liked any of the Tekkens, Tekken Dark Ressurection is an awesome fighting game, maybe the best fighter on a handheld. Particularly since the psp's d-pad isn't great for circular motions and Tekken doesn't require all that many of those.
Hot Shots gold 1 or 2, are great if you like golf games. Cartoony characters and pleasant style, but still plays good golf on interesting courses.
Crush is a very interesting game. It's a puzzle game, but not in the tetris sense. you control a character on a floating puzzle structure. You can take any angle and "crush" it to where it flattens to 2d, and the map adheres to the rules of that 2d view. So you have to get your guy to the exit of the map by cleverly switching perspective. But can be frustrating if you're not keen on the genre.
On a similar vein there's Echochrome. Basically you navigate a stick figure through various MC Eshcer like mind bending structures, where what you see is what you get. So you can move the structure around, and if it makes a staircase in one angle the stick figure can cross, but at a different angle your figure would plummet to his death. People say the soundtrack is one of the best, but it's not a genre that I'm in to.
Field Commander is a good strategy game that's like advance wars or a futuristic Panzer General if you like that genre. Square based with your usual assortment of tanks, infantry, artillery and whatnot. Solid game, with maybe some iffy AI.
Disgea is one of the better srpg's out there. A good system with an entertaining story.
Final Fantasy Tactics is one of my favorite games of all time. I loved the story, and the gameplay was really entertaining. Might be a bit simple for you compared to Jeanne D'Arc.
The Metal Gear Acid games are actually pretty good. Its like other Strategy Rpg's, only what you can do is based on card draws. So imagine Jeanne D'Arc, only what magic you can cast and weapons you can use are based on the cards you draw. You make your own deck and buy cards with in game currency. It adds the deck building strategy to the normal strategy rpg mix.
"Exit" is a side scrolling platformer game. Sort of a modern elevator action with more strategy. You're some expert on getting people out of dangerous buildings. So you walk around a 2d side scrolling building with various types of trapped people, and work to help them get out using strategy. So if you're going to push someone up to a higher ledge, you have to make sure they're strong enough to pull you up, while still worrying about the hysterical pansy that won't move without having their hand held. Not my genre but I hear it's really good.
Most home console genres are covered on the PSP, so if you really like something on your main console there's probably a portable version of it. But some people are against playing portable versions of console games.
Beats is a downloadable game that allows you to use any mp3 on your memory stick and play a rhythm game based on the beats in the music. Very fun and very cheap.
