The Collaborative International Dictionary of English v.0.48:

Drowsy \Drow"sy\, a. [Compar. Drowsier; superl. Drowsiest.]
   1. Inclined to drowse; heavy with sleepiness; lethargic;
      dozy. "When I am drowsy." --Shak.
      [1913 Webster]

            Dapples the drowsy east with spots of gray. --Shak.
      [1913 Webster]

            To our age's drowsy blood
            Still shouts the inspiring sea.       --Lowell.
      [1913 Webster]

   2. Disposing to sleep; lulling; soporific.
      [1913 Webster]

            The drowsy hours, dispensers of all good.
                                                  --Tennyson.
      [1913 Webster]

   3. Dull; stupid. " Drowsy reasoning." --Atterbury.

   Syn: Sleepy; lethargic; dozy; somnolent; comatose; dull
        heavy; stupid.
        [1913 Webster]

WordNet (r) 3.0 (2006):

drowsy
    adj 1: half asleep; "made drowsy by the long ride"; "it seemed a
           pity to disturb the drowsing (or dozing) professor"; "a
           tired dozy child"; "the nodding (or napping) grandmother
           in her rocking chair" [syn: drowsy, drowsing(a),
           dozy]
    2: showing lack of attention or boredom; "the yawning
       congregation" [syn: drowsy, oscitant, yawning(a)]

Moby Thesaurus II by Grady Ward, 1.0:

64 Moby Thesaurus words for "drowsy":
   anesthetized, appeasing, calming, cataleptic, comatose, cradling,
   doped, dozy, dreamy, drugged, drugged with sleep, gentling, groggy,
   half asleep, heavy, heavy with sleep, heavy-eyed, hushing,
   in a stupor, lackadaisical, languid, languorous, lazy, lethargic,
   listless, lulling, mollifying, napping, narcoleptic, narcose,
   narcotized, narcous, nodding, oscitant, out of it, pacifying,
   quietening, restful, rocking, sedated, sleep-drowned, sleep-drunk,
   sleep-filled, sleep-swollen, sleepful, sleepy, sluggish,
   slumberous, slumbery, snoozy, somnolent, soothful, soothing,
   soporific, stilling, stretchy, stuporose, stuporous, tired, torpid,
   tranquilizing, weary, yawning, yawny