The Collaborative International Dictionary of English v.0.48:

Grog \Grog\ (gr[o^]g), n. [So named from "Old Grog" a nickname
   given to Admiral Vernon, in allusion to his wearing a grogram
   cloak in foul weather. He is said to have been the first to
   dilute the rum of the sailors (about 1745).]
   A mixture of spirit and water not sweetened; hence, any
   intoxicating liquor.
   [1913 Webster]

   Grog blossom, a redness on the nose or face of persons who
      drink ardent spirits to excess. [Collog.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

grog
    n 1: rum cut with water

Moby Thesaurus II by Grady Ward, 1.0:

37 Moby Thesaurus words for "grog":
   John Barleycorn, alcohol, alcoholic beverage, alcoholic drink,
   aqua vitae, ardent spirits, beverage, booze, brew, drink,
   firewater, hard liquor, hooch, inebriant, intoxicant,
   intoxicating liquor, juice, liquor, little brown jug, potable,
   potation, punch bowl, rum, schnapps, social lubricant, spirits,
   strong drink, strong waters, the Demon Rum, the bottle, the cup,
   the flowing bowl, the luscious liquor, the ruddy cup, tipple,
   toxicant, water of life