Dragon Age is great as already mentioned. Tremendous flexibility for character design and interactions and a complex involving story.

FFXIII is visually stunning with a few great characters as well as some appalling amounts of linearity and restricted gameplay for the first two thirds of the game. Great for fans of delayed gratification.

I'm playing Ar Tonelico Qoga and I like it despite its numerous flaws. It's got an often juvenile sense of humor with a heavy emphasis on fanservice (female characters boost song magic by losing clothing although the male characters do as well when executing ultimate supermoves). Despite this the premise is interesting, the music is great, and the world design is neat. The characters are recognizable out of any anime, but relatable.

It's basically an RPG crossed with a dating sim. There are two main female characters the hero can interact with and Dive into their minds to unlock new powers, song magic and alternate personalities. Depending on player choices, it's possible to obtain multiple endings with them or even hook up with another character or two.

I enjoyed it enough to look up the first two Ar Tonelico games for the PS2. They might be a better place to start for this game series frankly. AT1 has the same basic scenario but with a lot less fanservice.