The Collaborative International Dictionary of English v.0.48:

Engaging \En*ga"ging\, a.
   Tending to draw the attention or affections; attractive; as,
   engaging manners or address. -- En*ga"ging*ly, adv. --
   En*ga"ging*ness, n.
   [1913 Webster]

   Engaging and disengaging gear or Engaging and disengaging
   machinery, that in which, or by means of which, one part is
      alternately brought into gear or out of gear with another
      part, as occasion may require.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Encage \En*cage"\, v. t. [imp. & p. p. Encaged; p. pr. & vb.
   n. Engaging.] [Pref. en- + cage: cf. F. encager.]
   To confine in a cage; to coop up. --Shak.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Engage \En*gage"\, v. t. [imp. & p. p. Engaged; p. pr. & vb.
   n. Engaging.] [F. engager; pref. en- (L. in) + gage pledge,
   pawn. See Gage.]
   1. To put under pledge; to pledge; to place under obligations
      to do or forbear doing something, as by a pledge, oath, or
      promise; to bind by contract or promise. "I to thee
      engaged a prince's word." --Shak.
      [1913 Webster]

   2. To gain for service; to bring in as associate or aid; to
      enlist; as, to engage friends to aid in a cause; to engage
      men for service.
      [1913 Webster]

   3. To gain over; to win and attach; to attract and hold; to
      draw.
      [1913 Webster]

            Good nature engages everybody to him. --Addison.
      [1913 Webster]

   4. To employ the attention and efforts of; to occupy; to
      engross; to draw on.
      [1913 Webster]

            Thus shall mankind his guardian care engage. --Pope.
      [1913 Webster]

            Taking upon himself the difficult task of engaging
            him in conversation.                  --Hawthorne.
      [1913 Webster]

   5. To enter into contest with; to encounter; to bring to
      conflict.
      [1913 Webster]

            A favorable opportunity of engaging the enemy.
                                                  --Ludlow.
      [1913 Webster]

   6. (Mach.) To come into gear with; as, the teeth of one
      cogwheel engage those of another, or one part of a clutch
      engages the other part.
      [1913 Webster]

WordNet (r) 3.0 (2006):

engaging
    adj 1: attracting or delighting; "an engaging frankness"; "a
           piquant face with large appealing eyes" [syn: engaging,
           piquant]

Moby Thesaurus II by Grady Ward, 1.0:

81 Moby Thesaurus words for "engaging":
   absorbing, agreeable, alluring, appealing, appetizing, arresting,
   attractive, beguiling, bewitching, blandishing, cajoling,
   captivating, catching, charismatic, charming, coaxing, come-hither,
   consuming, coquettish, delightful, dulcet, enchanting, engagement,
   engrossing, enravishing, enthralling, enticing, entrancing,
   exciting, exotic, exquisite, fascinating, fetching, flirtatious,
   friendly, glamorous, gripping, heart-robbing, hiring, holding,
   hypnotic, interesting, intriguing, inviting, irresistible,
   likeable, lovely, luxurious, magnetic, mesmeric, mesmerizing,
   mouth-watering, obsessing, obsessive, open, piquant, pleasant,
   pleasing, prepossessing, provocative, provoquant, ravishing,
   seducing, seductive, sensuous, siren, sirenic, spellbinding,
   spellful, taking, tantalizing, teasing, tempting, thrilling,
   tickling, titillating, titillative, voluptuous, winning, winsome,
   witching