The Collaborative International Dictionary of English v.0.48:

Fawn \Fawn\, v. i. [imp. & p. p. Fawned; p. pr. & vb. n.
   Fawning.] [OE. fawnen, fainen, fagnien, to rejoice,
   welcome, flatter, AS. f[ae]gnian to rejoice; akin to Icel.
   fagna to rejoice, welcome. See Fain.]
   To court favor by low cringing, frisking, etc., as a dog; to
   flatter meanly; -- often followed by on or upon.
   [1913 Webster]

         You showed your teeth like apes, and fawned like
         hounds.                                  --Shak.
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         Thou with trembling fear,
         Or like a fawning parasite, obeyest.     --Milton.
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         Courtiers who fawn on a master while they betray him.
                                                  --Macaulay.
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WordNet (r) 3.0 (2006):

fawning
    adj 1: attempting to win favor from influential people by
           flattery [syn: bootlicking, fawning, obsequious,
           sycophantic, toadyish]
    2: attempting to win favor by flattery [syn: bootlicking,
       fawning, sycophantic, toadyish]