The Collaborative International Dictionary of English v.0.48:

Dream \Dream\, v. i. [imp. & p. p. Dreamed (dr[=e]md) or
   Dreamt (dr[e^]mt); p. pr. & vb. n. Dreaming.] [Cf. AS.
   dr[=e]man, dr[=y]man, to rejoice. See Dream, n.]
   1. To have ideas or images in the mind while in the state of
      sleep; to experience sleeping visions; -- often with of;
      as, to dream of a battle, or of an absent friend.
      [1913 Webster]

   2. To let the mind run on in idle revery or vagary; to
      anticipate vaguely as a coming and happy reality; to have
      a visionary notion or idea; to imagine.
      [1913 Webster]

            Here may we sit and dream
            Over the heavenly theme.              --Keble.
      [1913 Webster]

            They dream on in a constant course of reading, but
            not digesting.                        --Locke.
      [1913 Webster]

WordNet (r) 3.0 (2006):

dreaming
    n 1: imaginative thoughts indulged in while awake; "he lives in
         a dream that has nothing to do with reality" [syn: dream,
         dreaming]
    2: a series of mental images and emotions occurring during
       sleep; "I had a dream about you last night" [syn: dream,
       dreaming]

Moby Thesaurus II by Grady Ward, 1.0:

78 Moby Thesaurus words for "dreaming":
   Walter Mitty, absence of mind, absent, absentminded,
   absentmindedness, absorbed, absorption, abstracted, abstractedness,
   abstraction, bemused, bemusement, brown study, castle-building,
   charmed, daydream, daydreamer, daydreaming, daydreamy,
   depth of thought, dream, dreamery, dreamful, dreamfulness,
   dreaminess, dreamlike, dreamlikeness, dreamy, dreamy-eyed,
   dreamy-souled, drowsing, ecstatic, elsewhere, enchanted, engrossed,
   engrossment, entranced, fantasy, fantasying, faraway,
   fit of abstraction, half-awake, in a reverie, in a trance,
   in the clouds, lost, lost in thought, meditative, mooning,
   moonraking, muse, museful, musefulness, musing, muted ecstasy,
   napping, nodding, oblivious, pensive, pensiveness, pipe dream,
   pipe-dreaming, preoccupation, preoccupied, rapt, reverie,
   somewhere else, spellbound, spelled, stargazing, study, taken up,
   trance, tranced, transported, unconscious, woolgathering,
   wrapped in thought