Chibi-Robo. It's a fun, quirky, cute...I guess you could call it a platformer. You play as a tiny robot who cleans up after and takes care of the mental well-being of the family who bought him, as well as the sentient toys that were given life by aliens. Okay, so it sounds like complete shit, but i assure you, it's a great game. It's quirky, it's fun, it's touching at moments. It's well worth the purchase.
Baten Kaitos - A JRPG that uses a unique card-based combat system. One of the best card-based systems I've used. It's fluid, intuitive, and works wonderfully. Also, the cards age, changing into different cards as time passes(not during combat. cards change only outside of combat, and can take anywhere from a few minutes to several days real time to change). It adds a nice level of depth to the system. The voice acting is shit, but you can turn it off. The story's actually pretty good. Oh, and the soundtrack is bitchin'.
Paper Mario: The Thousand Year Door. Fun story, simple but engaging combat. A must have game.
Resident Evil 4. If you've never played it, get it. Visually, it still holds up pretty well, and it's a really fun game.
Tales of Symphonia. An action JRPG with a great story. The voice acting is hit or miss. I thought it was okay, but others thought it was horrible. Combat's fun, story's great, characters are likable. What more can you ask for from a game?
Viewtiful Joe. Inventive Beat 'um Up that uses a rather unique art style akin to a comic book filmed on old film. With time-bending super powers, wonderfully cheesy story and dialog, it's an excellent game.
Eternal Darkness. I recommend you watch/read a couple reviews on this one before picking it up. It's one of those love it or hate it games. A horror game shown through the perspective of several characters, the story can be somewhat dry, and the combat is rather frustrating, but it's a very interesting game that I believe is worth a playthrough.