The Collaborative International Dictionary of English v.0.48:

Exasperate \Ex*as"per*ate\, v. t. [imp. & p. p. Exsasperated;
   p. pr. & vb. n. Exasperating.]
   1. To irritate in a high degree; to provoke; to enrage; to
      excite or to inflame the anger of; as, to exasperate a
      person or his feelings.
      [1913 Webster]

            To exsasperate them against the king of France.
                                                  --Addison.
      [1913 Webster]

   2. To make grievous, or more grievous or malignant; to
      aggravate; to imbitter; as, to exasperate enmity.
      [1913 Webster]

            To exasperate the ways of death.      --Sir T.
                                                  Browne.

   Syn: To irritate; provoke. See Irritate.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

exasperating \exasperating\ adj.
   1. extremely annoying or displeasing.

   Syn: annoying, infuriating, maddening, vexing.
        [WordNet 1.5]

   2. same as exacerbating.

   Syn: aggravating, exacerbating.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

exasperating
    adj 1: extremely annoying or displeasing; "his cavelier curtness
           of manner was exasperating"; "I've had an exasperating
           day"; "her infuriating indifference"; "the ceaseless
           tumult of the jukebox was maddening" [syn:
           exasperating, infuriating, maddening, vexing]
    2: making worse [syn: aggravating, exacerbating,
       exasperating]

Moby Thesaurus II by Grady Ward, 1.0:

35 Moby Thesaurus words for "exasperating":
   aggravating, aggravative, annoying, bothering, bothersome,
   contentious, disturbing, exasperative, galling, harassing,
   importunate, importune, irking, irksome, irritating, pesky,
   pestering, pestiferous, pestilent, pestilential, plaguesome,
   plaguey, plaguing, provocative, provoking, teasing, tiresome,
   tormenting, troublesome, troubling, vexatious, vexing, wearisome,
   worrisome, worrying