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.
      [1913 Webster]

            Boggling at nothing which serveth their purpose.
                                                  --Barrow.
      [1913 Webster]

   2. To do anything awkwardly or unskillfully.
      [1913 Webster]

   3. To play fast and loose; to dissemble. --Howell.
      [1913 Webster]

   Syn: To doubt; hesitate; shrink; stickle; demur.
        [1913 Webster]

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]

Moby Thesaurus II by Grady Ward, 1.0:

212 Moby Thesaurus words for "boggle":
   addle, amaze, around the bush, astonish, astound, awe, awestrike,
   back out, bad job, baffle, balk, bamboozle, bashfulness,
   be all thumbs, beat, beat about, bedaze, bedazzle, beef,
   beg the question, bevue, bewilder, bicker, bitch, blench, blow,
   blunder, blunder away, blunder into, blunder on, blunder upon,
   bobble, boggling, bollix, bonehead play, boner, boo-boo, botch,
   bowl down, bowl over, boycott, buffalo, bumble, bungle, butcher,
   call in question, cavil, challenge, chicken, chicken out,
   choplogic, clumsy performance, cobble, commit a gaffe, complain,
   compunction, confound, cry out against, daze, dazzle, demonstrate,
   demonstrate against, demur, demurral, desert under fire,
   diffidence, dispute, dodge, dumbfound, dumbfounder,
   enter a protest, equivocate, error, etourderie, evade,
   evade the issue, expostulate, falter, faltering, faux pas, fence,
   fight shy, fight shy of, flabbergast, flinch, floor, flounder,
   flub, fluff, foozle, fuddle, fumble, funk, funk out, gag,
   gaucherie, get, get cold feet, goof up, gum up, hang back,
   hang off, hash, have qualms, have two minds, hedge, hesitance,
   hesitancy, hesitate, hesitation, hold off, holler, howl, jib, jump,
   jump a mile, keep in suspense, kick, lick, lose courage, louse up,
   lumber, make bones about, mar, march, maze, mess, miscue, mistake,
   modesty, muddle, muff, murder, mystify, nitpick, nonplus, object,
   objection, obscure, off day, overwhelm, palter, panic, paralyze,
   parry, pause, perplex, petrify, pick nits, picket, play havoc with,
   press objections, prevaricate, protest, pull back, pussyfoot,
   puzzle, quail, qualm, qualm of conscience, qualmishness, quibble,
   raise a howl, rally, recoil, remonstrate, sad work, scruple,
   scrupulosity, scrupulousness, scuttle, shift, shrink, shrinking,
   shuffle, shy, shy at, shyness, sidestep, sit in, skedaddle, slip,
   split hairs, spoil, squawk, stagger, stampede, start, start aside,
   startle, state a grievance, stick, stick at, stickle, stickling,
   strain, strike, strike dead, strike dumb, strike with wonder,
   stumble, stump, stun, stupefy, surprise, teach in, tergiversate,
   throw, trip, waver, wince, yell bloody murder