late 14c., from rush (v.). Sense of "mass migration of people" (especially to a gold field) is from 1848, American English. Meaning "surge of pleasure" is from 1960s. Rush hour first recorded 1888.
mid-14c. (implied in rushing), "to drive back or down," from Anglo-French russher, from Old French ruser "to dodge, repel" (see ruse). Meaning "to do something quickly" is from 1650s; transitive sense of "to hurry up (someone or something)" is from 1850. Football sense originally was in rugby (1857). Fraternity/sorority sense is from 1896 (originally it was what the fraternity did to the student).
"plant growing in marshy ground," Old English resc, earlier risc, from Proto-Germanic *rusk- (cf. Middle Low German rusch, Middle High German rusch, West Frisian risk).
Old French rusche probably is from a Germanic source. Used for making torches and finger rings, also strewn on floors when visitors arrived; it was attested a type of "something of no value" from c.1300.