early 13c., from Anglo-French rivere, Old French riviere "river, riverside, river bank" (12c.), from Vulgar Latin *riparia "riverbank, seashore, river" (cf. Spanish ribera, Italian riviera), noun use of fem. of Latin riparius "of a riverbank" (see riparian). Generalized sense of "a copious flow" of anything is from late 14c. The Old English word was ea "river," cognate with Gothic ahwa, Latin aqua (see aqua-). Romanic cognate words tend to retain the sense "river bank" as the main one, or else the secondary Latin sense "coast of the sea" (cf. Riviera).
U.S. slang phrase up the river "in prison" (1891) is originally in reference to Sing Sing prison, which was literally "up the (Hudson) river" from New York City. Phrase down the river "done for, finished" perhaps echoes sense in sell down the river (1851), originally of troublesome slaves, to sell from the Upper South to the harsher cotton plantations of the Deep South.