The Collaborative International Dictionary of English v.0.48:

Groggy \Grog"gy\, a.
   1. Overcome with grog; tipsy; unsteady on the legs. [Colloq.]
      [1913 Webster]

   2. Weakened in a fight so as to stagger; -- said of
      pugilists. [Cant or Slang]
      [1913 Webster]

   3. (Man.) Moving in a hobbling manner, owing to tender feet;
      -- said of a horse. --Youatt. Grogram

WordNet (r) 3.0 (2006):

groggy
    adj 1: stunned or confused and slow to react (as from blows or
           drunkenness or exhaustion) [syn: dazed, foggy,
           groggy, logy, stuporous]

Moby Thesaurus II by Grady Ward, 1.0:

84 Moby Thesaurus words for "groggy":
   abeyant, addled, apathetic, baffled, bedazzled, befuddled,
   benumbed, bewildered, cataleptic, catatonic, confounded, confused,
   dazed, dazzled, dead, dilapidated, doddering, dopey, dormant, dull,
   faint, flat, foul, heavy, in a daze, in a stupor, in a trance,
   in abeyance, in suspense, inactive, inert, knocked silly, languid,
   languorous, latent, leaden, lifeless, logy, mazed, muddled, muzzy,
   numb, numbed, passive, phlegmatic, punch-drunk, punchy, puzzled,
   ramshackle, reeling, ricketish, rickety, rocky, sedentary, shaky,
   silly, slack, slaphappy, sleeping, sluggish, slumbering,
   smoldering, spidery, spindly, staggering, stagnant, standing,
   static, stunned, stupefied, suspended, tame, teetering, teetery,
   torpid, tottering, tottery, tumbledown, unaroused, unsteady, weak,
   weak-kneed, wobbly, woozy