Robot Alchemic Drive - you pilot a giant robot against giant monsters. Thing is, though, you're a wee squishy human. Your human controls the robot from afar, or on it's shoulder with a PS2 controller. Best game ever. Despite the intentionally awful English voices. Or because of? This may be hard to find, though.
Ace Combat 4,5, 0 - ridiculously anime "flight" sim. Nothing real about it at all in the Sim area other than some real planes. So fun, though. Don't think any of these are story sequels, so grabbing anyout of order won't confuse you.
Okami - Zelda-like game where you're a (I think it was...) a sun goddess named Ameratsu who is a wolf. Anyway, your moves in combat are executed by using brush strokes on a canvas. You use these in the exploring part, too. The Wii version might play better, but this game is awesome, either way. Though, it tricks you into thinking it's only like 8 hours long at first, then it opens the world up to like a 30 hour game.
Shin Megami Tensei: Persona 3&4 - RPGs. Not story sequels, though, so playing one or the other will get you a full story.
Sure there are others, but this is long enough, I think.