The Collaborative International Dictionary of English v.0.48:

Whine \Whine\, v. i. [imp. & p. p. Whined; p. pr. & vb. n.
   Whining.] [OE. whinen, AS. hw[imac]nan to make a whistling,
   whizzing sound; akin to Icel. hv[imac]na, Sw. hvina, Dan.
   hvine, and probably to G. wiehern to neigh, OHG. wih[=o]n,
   hweij[=o]n; perhaps of imitative origin. Cf. Whinny, v. i.]
   To utter a plaintive cry, as some animals; to moan with a
   childish noise; to complain, or to tell of sorrow, distress,
   or the like, in a plaintive, nasal tone; hence, to complain
   or to beg in a mean, unmanly way; to moan basely. "Whining
   plovers." --Spenser.
   [1913 Webster]

         The hounds were . . . staying their coming, but with a
         whining accent, craving liberty.         --Sir P.
                                                  Sidney.
   [1913 Webster]

         Dost thou come here to whine?            --Shak.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

84 Moby Thesaurus words for "whining":
   Jeremianic, acute, argute, bawling, beef, beefing, bellyache,
   bellyaching, bitch, bitching, blatant, complaining, complaint,
   creaky, crying, destructive criticism, dissent, ear-piercing,
   faultfinding, fretful, grievance, gripe, griping, groan, groaning,
   grouse, grousing, grumbling, holler, howl, howling, keen, keening,
   kick, kicking, lamentive, lowing, moanful, moaning, mournful,
   mugient, murmuring, peeve, peevish, peevishness, penetrating,
   pet peeve, petulance, petulant, piercing, piping, plaintive,
   plangent, protest, puling, querulous, querulousness, reedy,
   scolding, screaky, screeching, screechy, sharp, shrieking, shrieky,
   shrill, sigh, sighing, sniping, sobbing, sorrowful, soughing,
   squawk, squawking, squeaking, squeaky, thin, ululant, wailful,
   wailing, whimpering, whiny, whistling, yapping