The Collaborative International Dictionary of English v.0.48:

Banzai \Ban"zai"\, interj. [Jap. banzai, banzei, ten thousand
   years, forever.]
   Lit., May you live ten thousand years; -- used in salutation
   of the emperor and as a battle cry. [Japan]
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

banzai
    n 1: a Japanese cheer of enthusiasm or triumph

Moby Thesaurus II by Grady Ward, 1.0:

22 Moby Thesaurus words for "banzai":
   bugle call, call to arms, call-up, catchword, clarion,
   clarion call, conscription, exhortation, go for broke, gung ho,
   levy, mobilization, muster, rally, rallying cry, rebel yell,
   recruitment, slogan, trumpet call, war cry, war whoop, watchword