I'd say that it happens more than half the time in long-term games that I've participated in (not including instances anti-social acting out or actual fallings out between players).
A couple of the more memorable times, for me, have been...
In a campaign that I played in, I was playing a paladin, and another member of the party became demon-possessed somehow. Usually, the character was in control of himself, but rarely, the demon took possession, and set about wreaking havoc. My paladin was very confused, at first, because he would sometimes get 'false positives' from the demon-possessed character on the detect evil. That is, the character would detect as evil, but the paladin knew that the character was not evil, based on the character's deeds and words (they group had been traveling together for quite some time, and the two characters were friends, the paladin had witnessed the other character's goodness for himself). Eventually, the demon gave himself away to my paladin. So, with the help of another party member, we managed to beat him into submission and restrain him until the demon could be exorcised.
In a campaign that I ran, one of the party members was accused of intentionally letting a plague (a figurative one, in the form of an escaped bad guy) loose on a planet. The evidence did not look good (some members of the court having it out for the party) so, in a fit of good sense, the character demanded that he be granted the right of trial by combat (something that he could do, due to his character's background). He chose one of the other party members as his second. The court agreed, choosing the other two party members as its champions. The accused was victorious, but barely, even after a tiny bit of shenanigan on behalf of an interested third-party.
In both of these cases, it was clear that the conflict was between the characters, not the players. Tactics were used, stops were pulled out, wackiness ensued, and a good time was had by all.