The Collaborative International Dictionary of English v.0.48:

Satyr \Sa"tyr\ (?; 277), n. [L. satyrus, Gr. ?: cf. F. satyre.]
   1. (Class. Myth.) A sylvan deity or demigod, represented as
      part man and part goat, and characterized by riotous
      merriment and lasciviousness.
      [1913 Webster]

            Rough Satyrs danced; and Fauns, with cloven heel,
            From the glad sound would not be absent long.
                                                  --Milton.
      [1913 Webster]

   2. (Zool.) Any one of many species of butterflies belonging
      to the family Nymphalidae. Their colors are commonly
      brown and gray, often with ocelli on the wings. Called
      also meadow browns.
      [1913 Webster]

   3. (Zool.) The orang-outang.
      [1913 Webster]

WordNet (r) 3.0 (2006):

satyr
    n 1: man with strong sexual desires [syn: satyr, lecher,
         lech, letch]
    2: one of a class of woodland deities; attendant on Bacchus;
       identified with Roman fauns [syn: satyr, forest god]

Moby Thesaurus II by Grady Ward, 1.0:

47 Moby Thesaurus words for "satyr":
   Cailleac, Faunus, Pan, Priapus, Vidar, Vitharr, aphrodisiomaniac,
   bugger, coprophiliac, corn spirit, dirty old man, eroticomaniac,
   erotomaniac, exhibitionist, faun, fertility god, fetishist,
   field spirit, forest god, goat, gynecomaniac, lecher, masochist,
   narcissist, necrophiliac, nymphomaniac, old goat, panisc, panisca,
   paniscus, paraphiliac, pederast, pedophiliac, rapist, sadist,
   scotophiliac, silenus, sodomist, sodomite, sylvan deity,
   the goat god, transvestite, vegetation spirit, voyeur, whoremaster,
   whoremonger, zoophiliac



Easton's 1897 Bible Dictionary:

Satyr
   hairy one. Mentioned in Greek mythology as a creature composed
   of a man and a goat, supposed to inhabit wild and desolate
   regions. The Hebrew word is rendered also "goat" (Lev. 4:24) and
   "devil", i.e., an idol in the form of a goat (17:7; 2 Chr.
   11:15). When it is said (Isa. 13:21; comp. 34:14) "the satyrs
   shall dance there," the meaning is that the place referred to
   shall become a desolate waste. Some render the Hebrew word
   "baboon," a species of which is found in Babylonia.


The Devil's Dictionary (1881-1906):

SATYR, n.  One of the few characters of the Grecian mythology accorded
recognition in the Hebrew.  (Leviticus, xvii, 7.)  The satyr was at
first a member of the dissolute community acknowledging a loose
allegiance with Dionysius, but underwent many transformations and
improvements.  Not infrequently he is confounded with the faun, a
later and decenter creation of the Romans, who was less like a man and
more like a goat.