Games with good gameplay but terrible story that made you stop playing

[Zeh Don]

Grand Theft Auto IV bored me to tears, so I stopped playing and started Bioshock instead. Eventually went back to GTAIV, but I'd be lying if I said I enjoyed it.

Starcraft II: Wings of Liberty was pretty hard to finish, honestly. The story just kept getting worse. I refuse to replay that game - even for achievements - because the story is literally that bad.

Diablo III, however, drove me to stop playing on story alone. However, I was using my friend's account. If I'd paid for it, it might have been a different story.
After the Butcher boss fight, I was done. They'd managed to shit on every aspect of the original games, and I couldn't stomach it at all. Worst game I've ever played.

 

[Freakazoid]

I cannot think of ever having deserted a game simply because of bad story. I mean, I've experienced bad story telling, but if the game is fun, who cares? Like Kingdoms of Amalur was generic as all hell. But I'd just nod along and then get back to smacking prismere trolls with my epic hammer. Sleeping Dogs was meh, but when the fist-fighting and driving are so damn smooth, I can't bring myself to notice.
If I do leave a game with a bad story, it's because the gameplay was not engaging enough. Borderlands 2 was one of these for me. The game had great dialogue but suffered from repetitiveness and routine combat. I dropped it after a few gaming sessions cause I couldn't maintain interest.