Harden, one of five children, was born in La Jolla, California to Beverly Bushfield, a housewife, and Thaddeus Harold Harden, a Texas native who was an officer in the Navy. One of her siblings is also named Thaddeus. Harden's family frequently moved because of her father's job, living in Japan, Germany, Greece, California and Maryland. She graduated from Surrattsville High School in Clinton, Maryland in 1976 and from the University of Texas at Austin with a B.A. in theatre, earning an MFA from the graduate theatre program of New York University.

Harden debuted on Broadway in Tony Kushner's Angels in America in 1993. For her film work, she won a Best Supporting Actress Academy Award for Pollock (2000), and was nominated in the same category for Mystic River (2003). She is currently shooting a film called Home, in which she will be playing the role of a mother (to her real daughter, Eulala Scheel) as she did in Felicity: An American Girl Adventure (2005).

Other notable films include The Imagemaker (1986), her first screen role, in which she played a stage manager; the Coen Brothers' Miller's Crossing (1990), a 1930s mobster drama in which she gained her first wide exposure; the Disney sci-fi comedy Flubber (1997), a popular hit in which she co-starred with Robin Williams; the supernatural drama Meet Joe Black (1998); Labor of Love (1998), a Lifetime Television movie in which she starred with David Marshall Grant; and an all-star adventure-drama of aging astronauts, Space Cowboys (2000). She also guest-starred as a FBI undercover agent posing as a white-supremacist in "Raw," an episode of the popular crime drama Law & Order: Special Victims Unit for which she has been nominated for Best Guest Actress in a Drama Series. She recently reprised this role in the series' eighth season premiere.

Her nephew and niece, Sander and Audrey Harden, died in Astoria, New York of severe burns from a house fire, along with her former-sister-in-law, Rebecca.