I have a surprising amount of patience for things like this, especially if the game I'm trying is new to me. The only 2 games I ever put down and refused to keep playing ever, as opposed to put down and never got around to again, were Dragon Age: Origins and Zelda: Skyward Sword. I thought Dragon Age was a slog, accompanied by a dull art style, boring combat and woefully generic world. A couple of the characters were interesting, particularly Alistair and Morrigan, especially with the way they interacted with each other, but everything non-character-specific involving those two felt really stilted. As for Skyward Sword, it felt like there was nothing to the world; the surface locations are designed like mini-dungeons, rather than locations in the world, so visiting the same places continuously, over and over, after they've already been totally explored, felt like one of the worst design decisions that they could possibly make. Skyloft is the only remotely interesting area in the game. The new items (i.e. the Gust Bellows) are crappy and pretty useless aside from specific applications. The new bow is kinda cool, but the game is worse-off for not being able to lock onto and quickly fire arrows at enemies such as Keese. I could go on, but I'm starting to ramble. The fact of the matter is, it generally takes a lot of boredom to make me ditch a game before it "gets good".
I actually enjoyed Final Fantasy XIII to a degree. The aesthetics were phenomenal, with the visual and sound design being absolutely captivating. Most of the aspects of the game were sub-par, but honestly they weren't bad enough to stop me from playing, even if the corridor approach got kind of annoying after a while.