We called it "the Devil's Advocate" character, after the euphemism. One of my friends is really popular with this archetype. He ran a character who rolled such a bad charisma score that he decided to make him a cowardly warrior who couldn't stand the sight of blood. Obviously, while not a great character for combat situations, the gameplay was brilliant and hysterical as one of your sword-swinging companions starts shrieking out like a little-girl "Don't hurt me! Don't hurt me!" (this situation is verbatim).
Having such a polar opposite character (another term; not great, mind you) can be a blessing if the player is all for it, and an experienced player. I would not leave this to someone new to RPGs or to the group. Usually the effect is quite humorous, but many times it was a real pain as a quarter of our party was practically useless at everything except bad commentary and stating the painfully obvious.
Our DM created a feat called "Cowards' Cry" (the opposite of a battlecry) in which, if a coward screamed in terror and the attackers failed a Will check, they would be stunned for a number of rounds equal to 1/3 the level of the coward, in awe of the awesome shriek. This actually saved us a time or two, as it was an area-effect feat tailored for that character alone.