The Collaborative International Dictionary of English v.0.48:

Stupefy \Stu"pe*fy\, v. t. [imp. & p. p. Stupefied; p. pr. &
   vb. n. Stupefying.] [F. stup['e]fier, fr. L. stupere to be
   stupefied + ficare (in comp.) to make, akin to facere. See
   Stupid, Fact, and cf. Stupefacient.] [Written also
   stupify, especially in England.]
   1. To make stupid; to make dull; to blunt the faculty of
      perception or understanding in; to deprive of sensibility;
      to make torpid.
      [1913 Webster]

            The fumes of drink discompose and stupefy the brain.
                                                  --South.
      [1913 Webster]

   2. To deprive of material mobility. [Obs.]
      [1913 Webster]

            It is not malleable; but yet is not fluent, but
            stupefied.                            --Bacon.
      [1913 Webster]

WordNet (r) 3.0 (2006):

stupefy
    v 1: make dull or stupid or muddle with drunkenness or
         infatuation [syn: besot, stupefy]
    2: be a mystery or bewildering to; "This beats me!"; "Got me--I
       don't know the answer!"; "a vexing problem"; "This question
       really stuck me" [syn: perplex, vex, stick, get,
       puzzle, mystify, baffle, beat, pose, bewilder,
       flummox, stupefy, nonplus, gravel, amaze,
       dumbfound]
    3: make senseless or dizzy by or as if by a blow; "stun fish"
       [syn: stun, stupefy]

Moby Thesaurus II by Grady Ward, 1.0:

66 Moby Thesaurus words for "stupefy":
   KO, addle, amaze, anesthetize, appall, astonish, astound, awe,
   awestrike, bedaze, bedazzle, bemuse, benumb, besot, bewilder,
   blunt, boggle, bowl down, bowl over, chloroform, coldcock,
   confound, daze, dazzle, deaden, desensitize, dope, drug, dull,
   dumbfound, dumbfounder, etherize, faze, flabbergast, freeze,
   hebetate, horrify, kayo, knock out, knock senseless, knock stiff,
   knock unconscious, lay out, narcotize, nonplus, numb, obtund,
   overwhelm, palsy, paralyze, perplex, petrify, put to sleep, rattle,
   scare stiff, scare to death, shock, stagger, startle, strike dead,
   strike dumb, strike terror into, strike with wonder, stun,
   surprise, terrify