She has had a number of high-profile roles, including in the play Copenhagen on Broadway (for which she won a Tony Award in 2000), the leading actress in the films Altered States (1980), Continental Divide (1981) and Strapless (1989), as well as a run as the title character in the comedy-drama television series The Days and Nights of Molly Dodd, which ran from 1987 to 1991.

Her arguably highest profile film role to date was the romantic lead opposite John Belushi in Continental Divide (1981) for which she received her first Golden Globe Award nomination, in the category of Best Motion Picture Actress in a Comedy/Musical.

Other film roles include: And I Alone Survived (1978), Strapless (1989),[5][6] The Astronaut's Wife (1999), Clint Eastwood's Space Cowboys (2000), Lars von Trier's Dogville, the Kevin Bacon-directed Loverboy (2005) and The Sentinel (2006).

Brown received five consecutive Emmy Award nominations for each season, in the category of Outstanding Lead Actress in a Comedy Series, but never won.

Brown also appeared in several seasons of the Netflix comedy-drama series Orange is the New Black as fictional television personality Judy King, an inmate loosely based on Martha Stewart.

[8] Among her earlier roles was a run as Lucy Brown in the 1976 production of The Threepenny Opera, produced by Joe Papp and directed by Richard Foreman.

Her audiobooks projects include John Grisham's The Client, Lois Lowry's Number the Stars, Stephen King's Rose Madder, Kevin Henkes' Olive's Ocean, Sue Miller's 2005 novel Lost in the Forest, and Isabel Allende's Inés of My Soul.