The Collaborative International Dictionary of English v.0.48:

Mesmerize \Mes"mer*ize\, v. t. [imp. & p. p. Mesmerized; p.
   pr. & vb. n. Mesmerizing.] [Also spelled mesmerise.]
   1. To bring into a state of mesmeric sleep; to hypnotize.
      [1913 Webster]

   2. To produce an intense fascination in; to spellbind.
      [PJC]

WordNet (r) 3.0 (2006):

mesmerize
    v 1: attract strongly, as if with a magnet; "She magnetized the
         audience with her tricks" [syn: magnetize, mesmerize,
         mesmerise, magnetise, bewitch, spellbind]
    2: induce hypnosis in [syn: hypnotize, hypnotise,
       mesmerize, mesmerise]

Moby Thesaurus II by Grady Ward, 1.0:

60 Moby Thesaurus words for "mesmerize":
   absorb, absorb the attention, anesthetize, arrest, becharm,
   beguile, bewitch, captivate, carry away, cast a spell, catch,
   catch up, charm, dominate, dope, drug, enchant, engage,
   engage the attention, engage the mind, engage the thoughts,
   engross, engross the mind, engross the thoughts, enrapture,
   enravish, enthrall, entrance, exercise, fascinate, grab, grip,
   hold, hold spellbound, hold the interest, hypnotize, immerse,
   infatuate, intrigue, involve, involve the interest, lull to sleep,
   magnetize, monopolize, narcotize, obsess, occupy,
   occupy the attention, preoccupy, put to sleep, put under,
   rock to sleep, sedate, spell, spellbind, take up, trance,
   transport, vamp, witch