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"

Moby Thesaurus II by Grady Ward, 1.0:

157 Moby Thesaurus words for "blase":
   Laodicean, Olympian, aloof, apathetic, ataractic, benumbed, blah,
   bored, carefree, careless, casual, comatose, cool, cosmopolitan,
   cosmopolite, dead, debilitated, degage, desensitized, detached,
   devil-may-care, disabused, disappointed, disenchanted,
   disillusioned, disinterested, dispassionate, dispirited,
   disregardful, dopey, dormant, droopy, drugged, dull, easy,
   easygoing, emotionless, enervated, enlightened, exanimate,
   experienced, fed-up, free and easy, good and tired, heartless,
   heavy, hebetudinous, heedless, hopeless, in a stupor, inanimate,
   inattentive, incurious, indifferent, inert, inexcitable,
   insouciant, irked, jaded, knowing, lackadaisical, languid,
   languorous, leaden, lethargic, life-weary, lifeless, light-hearted,
   listless, lumpish, mature, matured, melancholic, melancholy,
   mindless, mondaine, moribund, negligent, nonchalant,
   not born yesterday, numb, numbed, offhand, old, passive,
   perfunctory, phlegmatic, pluckless, pococurante, pooped, practiced,
   put straight, reckless, regardless, resigned, ripe, ripened,
   robbed of illusion, sagacious, sated, satiated, seasoned,
   set right, sick, sick of, slack, sleepy, slow, sluggish, somnolent,
   sophisticate, sophisticated, soporific, spiritless, splenetic,
   spunkless, stagnant, stagnating, stoic, stultified, stupefied,
   supercilious, superior, supine, tired, tired of, tired of living,
   tired to death, torpid, tried, tried and true, turned-off,
   unanxious, uncaring, uncharmed, unconcerned, undeceived,
   undiscriminating, unimpressed, uninterested, unmindful, unmoved,
   unsolicitous, unspelled, vegetable, vegetative, veteran, wan,
   wearied, weariful, weary, weary unto death, withdrawn, world-weary,
   world-wise, worldly, worldly-wise