This thread is a great read, seeing how games can affect people so much.
For me it was Spec Ops: The Line. I didn't actually stop playing but didn't want to complete the story (had to really). I mean, I had heard it was a great story with mediocre gameplay but that hadn't actually prepared me to how much in the end I hated the guy I was playing.
I have never stopped playing a game because of a bad story, I've stopped because of interest going elsewhere or because of other bad aspects of games but never a story.