The Collaborative International Dictionary of English v.0.48:

Blas'e \Bla*s['e]"\ (bl[.a]*z[asl]"), a. [F., p. p. of blaser.]
   1. Having the sensibilities deadened by excess or frequency
      of enjoyment; sated or surfeited with pleasure;
      uninterested because of frequent exposure or indulgence;
      used up.

   Syn: bored.
        [1913 Webster + WordNet 1.5]

   2. very sophisticated; versed in the ways of the world. the
      blase traveler refers to the ocean he has crossed as `the
      pond'

   Syn: knowing, worldly.
        [WordNet 1.5]

   3. uninterested and attaching little importance; -- of
      attitudes toward duties. a blase attitude about
      housecleaning

   Syn: unconcerned.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

blase
    adj 1: very sophisticated especially because of surfeit; versed
           in the ways of the world; "the blase traveler refers to
           the ocean he has crossed as `the pond'"; "the benefits of
           his worldly wisdom" [syn: blase, worldly]
    2: uninterested because of frequent exposure or indulgence; "his
       blase indifference"; "a petulant blase air"; "the bored gaze
       of the successful film star" [syn: blase, bored]
    3: nonchalantly unconcerned; "a blase attitude about
       housecleaning"