Old English ridan "sit or be carried on" (as on horseback), "move forward; rock; float, sail" (class I strong verb; past tense rad, past participle riden), from Proto-Germanic *ridan (source also of Old Norse riða, Old Saxon ridan, Old Frisian rida "to ride," Middle Dutch riden, Dutch rijden, Old High Germn ritan, German reiten), from PIE *reidh- "to ride" (source also of Old Irish riadaim "I travel," Old Gaulish reda "chariot"). Common to Celtic and Germanic, perhaps a loan word from one to the other.
Meaning "heckle" is from 1912; that of "have sex with (a woman)" is from mid-13c.; that of "dominate cruelly" is from 1580s. To ride out "endure (a storm, etc.) without great damage" is from 1520s. To ride shotgun is by 1919, from custom of having an armed man beside the driver on the stagecoach in Old West movies to ward off trouble. To ride shank's mare "walk" is from 1846 (see shank (n.)).