"female horse," Old English mere (Mercian), myre (West Saxon), fem. of mearh "horse," from Proto-Germanic *markhjon- (source also of Old Saxon meriha, Old Norse merr, Old Frisian merrie, Dutch merrie, Old High German meriha, German Mähre "mare"), said to be of Gaulish origin (compare Irish and Gaelic marc, Welsh march, Breton marh "horse"). No known cognates beyond Germanic and Celtic. As the name of a throw in wrestling, it is attested from c. 1600. Mare's nest "illusory discovery, excitement over something which does not exist" is from 1610s.
"broad, dark areas of the moon," 1765, from Latin mare "sea" (from PIE root *mori- "body of water"); applied to lunar features by Galileo and used thus in 17c. Latin works. They originally were thought to be actual seas.
"night-goblin, incubus," Old English mare "incubus, nightmare, monster," from mera, mære, from Proto-Germanic *maron "goblin" (source also of Middle Low German mar, Middle Dutch mare, Old High German mara, German Mahr "incubus," Old Norse mara "nightmare, incubus"), from PIE *mora- "incubus" (source also of first element in Old Irish Morrigain "demoness of the corpses," literally "queen of the nightmare," also Bulgarian, Serbian mora, Czech mura, Polish zmora "incubus;" French cauchemar, with first element from Old French caucher "to trample"), from root *mer- "to rub away, harm" (also "to die" and forming words referring to death and to beings subject to death).