Joseph Edward Brennan (born November 2, 1934) is an American politician from Maine and a Democrat.

Brennan attended Boston College and the University of Maine School of Law, and became Cumberland County District Attorney before winning election to the Maine House of Representatives (1965–1971) and State Senate (1973–1975). His first statewide candidacy was for Governor in 1974; he lost the Democratic nomination to George J. Mitchell. Appointed State Attorney General in 1975, Brennan ran for Governor again in 1978, winning the primary and general elections. Brennan was reelected in 1982, serving as Governor from 1979 to 1987. In 1986 he ran for the U.S. House in Maine's First Congressional District and won with 53% of the vote.

After two terms in the House, Brennan ran for Governor again in 1990, losing to Republican John McKernan with 44% of the vote. He ran again in 1994, losing to Independent Angus King with 34% of the vote but placing second, ahead of Republican Susan Collins. He would face Collins in another statewide election in 1996, running for the U.S. Senate seat being vacated by Bill Cohen; he lost, 49%-44%.