mid-14c., junke "old cable or rope," cut in bits and used for caulking, etc., a nautical word of uncertain origin, perhaps from Old French junc "rush, reed," also used figuratively as a type of something of little value, from Latin iuncus "rush, reed" (but OED finds "no evidence of connexion").
It was extended to "old refuse from boats and ships" (1660s), then to "old or discarded articles of any kind" (1884), usually with a suggestion of reusability. Meaning "salt meat used on long voyages" is from 1762. Meaning "narcotic drug" is from 1925. Junk food is from 1971; junk art is from 1961; junk mail first attested 1954; junk bond from 1979.