I am a gamer..... So much so that I am also in college in order to go into game design and concept art haha!
My games I love:
Monster hunter, psychonauts, fall out 3, assassin's creed, the sims (1, 2, and 3), little big planet, knights of the old republic, mario (anything), most nintendo 64 games, pokemon(any), phoenix wright (including apollo justice and ace investigations), some facebook games(happy pets/aquarium, etc.), some casual fun games like cooking mama, oblivion, age of empires, golden sun, harvest moon(any), and many more I can't think of..
I would suggest any of those games to be played by ANYONE. Especially psychonauts..Since they are trying to make a sequel right now but need to be sure there is enough interest XD oh goodness, I've been waiting 5 years for a sequel!
I prefer console games on the computer--I have a controller for the computer and having it on there allows for faster game updates(fixed glitches easy to download) or even hacks and mods(like costumes people made)... also you can insert your own music into the game that way which is a blast. But I am a handheld addict as well, especially for casual games for fun--harvest moon for instance, I love it on the ds, EXCELLENT game. Only the boy version though, it has glitches to manipulate that helps because the game was designed to be far too hard, the girl fixed version is a pain in the butt.
For the PSP, nothing beats monster hunter unite. That game changed the way I see monsters, and changed the way I design them. So good!