The game I played:
RPG/Adventure
* Star Ocean 4: (RPG) it's the prequel, the start of the series, so it's good to start with this one
* 3D Dot Game Heroes: (Adventure) A Zelda 1 (intentional) clone, but in 3D. with dungeons, city, missions.
* Eternal Sonata : (RPG) A RPG based on Chopin's life. A mix of fantasy and historical element (there are real pictures and narrator explaining Chopin's life between chapter).
* Catherine: (Text RPG/puzzle) a more adult story, you need to solve the hero's current situation by choosing how he should act after dumping his girlfriend.
* Atelier Rorona: (RPG/Text RPG) If you like the Atelier series. It's about alchemy and creating objects. most part is a text RPG, and a little part RPG with battles.
Action
* Castlevania ~ Lords of Shadow: Great Action game, with some backtrack. not RPG, and a new story (a story reboot, nothing related to previous Castelvania games)
* Prince of Persia: if you know the recent PoP games, it's the same style. though this one is not linear, you play in your own order.
* Alice madness returns: a revisited story of Alice in Wonderland. The game also feature the old (1997?) first game in the series "Alice madness".
The one I didn't play:
* Disgaea 3 and 4 : Tactical RPG
* Valkyria Chronicle : Tactical RPG
* Tales of Grace F: RPG
* Folklore: RPG/action?
* Darksider: Action
* Assassin Creed: Action
* Uncharted series
* FF13
That's all I remember for the moment.
edit:
I also like Katamari and Wipeout (though, it's neither action/RPG/Adventure)