From my own collection, I suggest:
Loco Roco (1 & 2) & Patapon - very colourful, energetic games to pass the time with. Loco Roco definitely 'feels' childish but is the most powerful anti-depressant I've ever known. Patapon, meanwhile, is stylish and rather difficult but kinda cool.
Lumines II - you will never need another puzzle game again
Every Extend Extra - It's a weird pseudo-shmup arcade... something... but it's awesome. You kill stuff by self-destructing!
Castlevania Dracula X Chronicles - Because it's a remake of Rondo of Blood, and you can unlock Symphony of the Night.
Star Ocean: First Departure & Second Evolution - JRPGs.
Valkyrie Profile Lenneth - Also JRPG, but with far more class.
FF7 Crisis Core - Or if you prefer a showy JRPG...
Prinny: Can I Really Be The Hero - Infuriatingly difficult but awesome platformer.
Me & My Katamari - Why not?
Guitaroo Man Lives! - Just in case you need a music game.