Berserk
Berserk (暴走, bousou) is a state in which an Evangelion has gone beyond Nerv's ability to control it. During these incidents, the Eva's resident soul appears to bypass restraint mechanisms and wield her own body, although it's arguable how much "conscious control" she has over the Eva's actions. (The discrepancy between the behavior of Yui Ikari and her Evangelion incarnation is often cited to this effect.) A berserk Evangelion can inexplicably continue to function even after its internal power batteries have been drained, and thus continue to operate beyond the established operational time limit. Frequently when an Evangelion goes berserk, it will violently snap open its wired-shut jaws.
Only Eva Unit 01 really goes "berserk" during the series: when fighting Sachiel, Leliel (with absolutely no internal power), Bardiel, and Zeruel (with no internal power). Eva Unit 00 does lose control on two occassions (in Episode 05 and Episode 14), but this was not in combat, and once its internal power supply ran out it stopped moving (it is not clear if this would properly be classified as "berserker" mode).
Eva Unit 02 was able to briefly go "berserk" in The End of Evangelion, allowing Asuka to continue to move it even after its internal power supply was drained and it had suffered mortal injuries. However, this was too late to allow it to win the fight against the Mass Production Evangelions.
This article bears the unpleasant designation of "Stub." This is a Bad Thing. Provide a great service to NGE fan-geeks everywhere by making it awesomer!