Satyr

Overview

A creature from Greek mythology, like the Centaur and Minotaur. Satyrs appear as bearded human men with the horns, legs and tails of goats. Their obscure cousins are Fauns (gentler, younger versions of them who aren't such lushes) and Ipotanes (men with the ears, legs and tails of horses). They're associated with the demigods Pan (the son of Hermes and a nameless nymph) and Silenus (an minor demigod who attends Dionysius, god of wine and merriment). Incurable drunkards, hornballs and party-animals, satyrs generally live to get drunk, party, and shag any woman they can get into bed. They're notorious for chasing after nymphs, who typically prefer the gentler, less insatiable, more refined and less stinking-drunkard fauns instead.

Dungeons & Dragons

Has appeared as almost a footnote in most editions of D&D. Typically associated with nymphs to the point of being the "male equivalent"; using their Charm-inducing panpipes to bewitch minions and seduce women, and breeding with nymphs to father more of both races.

You can play one in 3.5, though that Level Adjustment is a bitch.

Got promoted to a full playable race in 4e, via their Heroes of the Feywild sourcebook, which also gave players the side-note that if you want to rework the species into not being an all-male one in your game, go right ahead.

Pathfinder has both Satyrs and Fauns as enemies in their assorted bestiaries, with fauns being the more civilized breed (for a rather lenient definition of "civilized").

Monstergirls

As one of the more overwhelmingly masculine races in mythology, monstergirl depictions are surprisingly rare. They are typically avid party-girls and lusty booze-hounds, usually extremely busty, and by definition easy to screw. User beware, however; it's far from unheard of for monstergirl versions of satyrs to also be dickgirls.