The Collaborative International Dictionary of English v.0.48:

Boggle \Bog"gle\, v. i. [imp. & p. p. Boggled; p. pr. & vb. n.
   Boggling.] [ See Bogle, n.]
   1. To stop or hesitate as if suddenly frightened, or in
      doubt, or impeded by unforeseen difficulties; to take
      alarm; to exhibit hesitancy and indecision.
      [1913 Webster]

            We start and boggle at every unusual appearance.
                                                  --Glanvill.
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            Boggling at nothing which serveth their purpose.
                                                  --Barrow.
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   2. To do anything awkwardly or unskillfully.
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   3. To play fast and loose; to dissemble. --Howell.
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   Syn: To doubt; hesitate; shrink; stickle; demur.
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The Collaborative International Dictionary of English v.0.48:

Boggle \Bog"gle\, v. t.
   To embarrass with difficulties; to make a bungle or botch of.
   [Local, U. S.]
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Bogle \Bo"gle\, n. [Scot. and North Eng. bogle, bogill, bugill,
   specter; as a verb, to terrify, fr. W. bwgwl threatening,
   fear, bwg, bwgan, specter, hobgoblin. Cf. Bug.]
   A goblin; a specter; a frightful phantom; a bogy; a bugbear.
   [Written also boggle.]
   [1913 Webster]

WordNet (r) 3.0 (2006):

boggle
    v 1: startle with amazement or fear
    2: hesitate when confronted with a problem, or when in doubt or
       fear
    3: overcome with amazement; "This boggles the mind!" [syn:
       flabbergast, boggle, bowl over]