I've quit a few bands over the years - for exactly the reasons listed elsewhere, musical differences/personality clashes/crap gigs and live performances. There is one which is a tad different; the singer became a born again Christian then used the band as a vehicle to preach from. It was like Creed II. As an atheist who feels that religion causes more trouble that it's worth this didn't sit well with me. Asked the singer not to bring religion into it but he refused. Unlike the other band members who were also atheist but preferred not to rock the boat (we were a cracking originals band who had begun to build up a following) I couldn't continue and quit. It was a great shame and it left me hugely frustrated at the time.
Incidentally the singer, who is a lovely guy, has contacted be a couple of times since the band folded (well over 10 years ago), to ask if I would re-join as they are looking to get the original line up back together but I just have no appetite for it, despite the cool songs with bass lines I was very much proud of at the time.