So basically I'm looking for titles that are either so unique or so timeless or have such modern gameplay that you would recommend them to someone not neccessarily looking for a retro experience with the PSP.
These are the ones I've already compiled:
- SSX On Tour (Wintersports, more zen than arcady)
- Metal Gear Acid 1&2 (Tactics-focused deckbuilder, ahead of its time)
- LUMINES (Tetris from a different timeline)
- Chili con Carnage (Shoot-Em-Up that kinda controls like og Doom but 3rd person, tbh the humor is where it shines)
- Armored Core Formula Front (You're some kind of arena robot mechanic, the battles can play out with or without your input and you mostly customize the robots in between fights)
- Thrillville (You manage themeparks, unspectacular concept but pretty unique execution)
- Me & My Katamari (A classic, you roll a ball that grows in size as it accumulates various objects)
- Dead Head Fred (Action platformer with a few flaws but decent mechanics and story)
- GTA Chinatown Wars (Drugdealer Simulator before it was cool)
- Gladiator Begins (You're a gladiator fighting to pay off your debts and later the story can branch into several directions, very satisfying gameplay loop and makes the most of its small scale)
- LocoRoco 1&2 (The sidescroller for people who don't like sidescrollers)
- Daxter (Classic 3D platformer, many little features to keep you hooked)
- MediEvil (Classic Hack & Slash, nice atmosphere and some high quality jokes)
A lot of good titles have already been mentioned but holy crap no one said MotorStorm: Arctic Edge? Such a great racer, very polished and it has unique mechanics and a ton of fun vehicles to make it worth your while.
Also: Ace Combat X: Skies of Deception. If you're looking for an arcade flight sim, this one is for you. (I'd steer clear of it's successor Joint Assault though.)