The Collaborative International Dictionary of English v.0.48:

Bragger \Brag"ger\, n.
   One who brags; a boaster.
   [1913 Webster]

WordNet (r) 3.0 (2006):

bragger
    n 1: a very boastful and talkative person [syn: bragger,
         braggart, boaster, blowhard, line-shooter,
         vaunter]