Here's a list of a few (For the PS2):
Beyond Good and Evil - Solid story and blend of stealth and combat.
Drakengard - The game of my tween years, this is a RPG hack n slash/flight simulator with some fantasy and horror dashed in. While the combat may be repetitive to some, I found it very much worth the mad story and characters. Also, it turns the typical idea of the JRPG protagonist and turns it on it's head. I love it so.
Killer7 - Pretty much define Suda51's fame for strangeness and style; this game is a strange blend of First Person Shooting, Psychological Horror and Mind Screw; with wacky characters and a story that makes jack squat for sense.
Psychonauts - Yahtzee has covered this one, but I'll throw in my two cents by saying that the characters really are the heart of this game. Each person you encounter will react differently for each item/event/whatever that occurs around you. To put forth a point, the Dev team even had each character record lines for an item that would only last a few minutes in your inventory, unless you ran back to show said characters.
Radiata Stories - Great humor, hilarious characters and a solid combat system. Everything I love in a JRPG.