The Collaborative International Dictionary of English v.0.48:

Crow \Crow\ (kr[=o]), v. i. [imp. Crew (kr[udd]) or Crowed
   (kr[=o]d); p. p. Crowed (Crown (kr[=o]n), Obs.); p. pr. &
   vb. n. Crowing.] [AS. cr[=a]wan; akin to D. kraijen, G.
   kr[aum]hen, cf. Lith. groti to croak. [root]24. Cf. Crake.]
   1. To make the shrill sound characteristic of a cock, either
      in joy, gayety, or defiance. "The cock had crown."
      --Bayron.
      [1913 Webster]

            The morning cock crew loud.           --Shak.
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   2. To shout in exultation or defiance; to brag.
      [1913 Webster]

   3. To utter a sound expressive of joy or pleasure.
      [1913 Webster]

            The sweetest little maid,
            That ever crowed for kisses.          --Tennyson.
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   To crow over, to exult over a vanquished antagonist.
      [1913 Webster]

            Sennacherib crowing over poor Jerusalem. --Bp. Hall.
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The Collaborative International Dictionary of English v.0.48:

crowing \crowing\ adj.
   1. same as bragging.

   Syn: boastful, braggart(prenominal), bragging(prenominal),
        braggy, big, cock-a-hoop, self-aggrandizing,
        vainglorious.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

crowing
    adj 1: exhibiting self-importance; "big talk" [syn: boastful,
           braggart(a), bragging(a), braggy, big,
           cock-a-hoop, crowing, self-aggrandizing, self-
           aggrandising]
    n 1: an instance of boastful talk; "his brag is worse than his
         fight"; "whenever he won we were exposed to his gasconade"
         [syn: brag, bragging, crow, crowing, vaporing,
         line-shooting, gasconade]