Rasche graduated from Elmhurst College in 1966; his grandfather was also an alumnus. Coming from "a long line of Evangelical and United Church of Christ ministers", he attended the University of Chicago Divinity School for two years, then quit. He did, however, receive a graduate degree in English from University of Chicago.

After Second City, he starred in the Organic Theater's 1974 production of David Mamet's Sexual Perversity in Chicago, which established the playwright's characteristic blend of earthy, sometimes brutal dialogue.

He met his Future wife Heather Lupton after he moved to New York City in 1976. She has taught acting at University of California, Santa Barbara. Lupton made a guest appearance in the series Sledge Hammer as Hammer's ex-wife. They have three children.

He began appearing on television and films in 1977, making his film debut in 1978 in An Unmarried Woman, directed by Paul Mazursky. The following year, he had a small part in Woody Allen's Manhattan.

Rasche played Petruchio to Frances Conroy's Kate in a production of Shakespeare's Taming of the Shrew directed by Zoe Caldwell at the American Shakespeare Theatre in Stratford, Connecticut in the mid-1980s.

He played a terrorist in the 1983 television film Special Bulletin. He appeared on the Miami Vice episode "Bushido" (first aired November 22, 1985) as a KGB agent attempting to capture a former colleague of Lt. Castillo (Edward James Olmos). Ironically, during his subsequent starring role on Sledge Hammer! his character would often make jokes about Miami Vice.

Rasche is best known for his portrayal of the title character in the satirical television sitcom Sledge Hammer!, which ran from 1986 to 1988. The show was a spoof of police dramas and concerned the character Sledge Hammer, a violent and chauvinistic police inspector with a taste for large and powerful weaponry.

Rasche was lead character Buddy Wheeler in the 1990 Biker Comedy Masters of Menace.

Rasche played the role of Ted Forstmann in the 1993 made-for-television movie Barbarians at the Gate, about the leveraged buyout (LBO) of RJR Nabisco.

Rasche appeared in the TV Land series Impastor in the role of Alden Schmidt. Rasche appeared on the short-lived 2001 television series DAG as President Whitman, the President of the United States.

He portrayed Donald Greene, one of the passengers of United Airlines FLIGHT 93, in Paul Greengrass' 2006 9/11 film United 93.

Rasche joined the cast of Ugly Betty in its third season in 2009 as the wealthy father of Matt Hartley, Betty's love interest. He appeared in the final five episodes of season three, and remained in the cast until mid-season four when his character's arc ended.

Starting February 14, 2017 he played George Antrobus in Theatre for a New Audience's production of Thornton Wilder's The Skin of Our Teeth, opposite Kecia Lewis as Maggie Antrobus.