The Collaborative International Dictionary of English v.0.48:

Baffle \Baf"fle\ (b[a^]f"f'l), v. t. [imp. & p. p. Baffled
   (-f'ld); p. pr. & vb. n. Baffling (-fl[i^]ng).] [Cf.
   Lowland Scotch bauchle to treat contemptuously, bauch
   tasteless, abashed, jaded, Icel. b[=a]gr uneasy, poor, or
   b[=a]gr, n., struggle, b[ae]gja to push, treat harshly, OF.
   beffler, beffer, to mock, deceive, dial. G. b[aum]ppe mouth,
   beffen to bark, chide.]
   [1913 Webster]
   1. To cause to undergo a disgraceful punishment, as a
      recreant knight. [Obs.]
      [1913 Webster]

            He by the heels him hung upon a tree,
            And baffled so, that all which passed by
            The picture of his punishment might see. --Spenser.
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   2. To check by shifts and turns; to elude; to foil.
      [1913 Webster]

            The art that baffles time's tyrannic claim.
                                                  --Cowper.
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   3. To check by perplexing; to disconcert, frustrate, or
      defeat; to thwart. "A baffled purpose." --De Quincey.
      [1913 Webster]

            A suitable scripture ready to repel and baffle them
            all.                                  --South.
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            Calculations so difficult as to have baffled, until
            within a . . . recent period, the most enlightened
            nations.                              --Prescott.
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            The mere intricacy of a question should not baffle
            us.                                   --Locke.
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   Baffling wind (Naut.), one that frequently shifts from one
      point to another.
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   Syn: To balk; thwart; foil; frustrate; defeat.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Baffling \Baf"fling\ (b[a^]f"fl[i^]ng), a.
   Frustrating; discomfiting; disconcerting; as, baffling
   currents, winds, tasks. -- Baff"ling*ly, adv. --
   Baff"ling*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

baffling
    adj 1: making great mental demands; hard to comprehend or solve
           or believe; "a baffling problem"; "I faced the knotty
           problem of what to have for breakfast"; "a problematic
           situation at home" [syn: baffling, elusive, knotty,
           problematic, problematical, tough]

Moby Thesaurus II by Grady Ward, 1.0:

21 Moby Thesaurus words for "baffling":
   bewildering, bothering, confounding, confusing, defeating,
   discomposing, disconcerting, dismaying, distracting, disturbing,
   embarrassing, enigmatic, frustrating, intricate, mysterious,
   mystifying, perplexing, perturbing, problematic, puzzling,
   upsetting