The Collaborative International Dictionary of English v.0.48:

Sleepy \Sleep"y\, a. [Compar. Sleepier; superl. Sleepiest.]
   [AS. sl?pig. See Sleep, n.]
   1. Drowsy; inclined to, or overcome by, sleep. --Shak.
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            She waked her sleepy crew.            --Dryden.
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   2. Tending to induce sleep; soporiferous; somniferous; as, a
      sleepy drink or potion. --Chaucer.
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   3. Dull; lazy; heavy; sluggish. --Shak.
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            'Tis not sleepy business;
            But must be looked to speedily and strongly. --Shak.
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   4. Characterized by an absence of watchfulness; as, sleepy
      security.
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   Sleepy duck (Zool.), the ruddy duck.
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WordNet (r) 3.0 (2006):

sleepy
    adj 1: ready to fall asleep; "beginning to feel sleepy"; "a
           sleepy-eyed child with drooping eyelids"; "sleepyheaded
           students" [syn: sleepy, sleepy-eyed, sleepyheaded]

Moby Thesaurus II by Grady Ward, 1.0:

99 Moby Thesaurus words for "sleepy":
   anesthetized, apathetic, asleep, beat, benumbed, blase, bored,
   boring, cataleptic, comatose, dazed, dead, debilitated, doped,
   dopey, dormant, dozy, dreamy, droopy, drowsy, drugged,
   drugged with sleep, dull, enervated, exanimate, exhausted,
   fatigued, half asleep, heavy, heavy with sleep, heavy-eyed,
   hebetudinous, hypnotic, idle, in a stupor, inactive, inanimate,
   inert, jaded, knocked out, lackadaisical, languid, languorous,
   leaden, lethargic, lifeless, listless, lumpish, moribund, napping,
   narcoleptic, narcose, narcotic, narcotized, narcous, nodding, numb,
   opiate, oscitant, out, out of it, passive, phlegmatic, pooped,
   quiet, sated, sedated, sleep-drowned, sleep-drunk, sleep-filled,
   sleep-swollen, sleepful, sleeping, slow, sluggish, slumbering,
   slumberous, slumbery, snoozy, somnifacient, somniferous, somnolent,
   soporific, stagnant, stagnating, stretchy, stultified, stuporose,
   stuporous, supine, tired, torpid, vegetable, vegetative, wan,
   weary, world-weary, yawning, yawny