Nance married Catherine E. Coulson in 1968, but the couple divorced in 1976. In May 1991, he married Kelly Jean Van Dyke (who worked in the adult film industry under the name Nancee Kelly). Van Dyke was the daughter of Jerry Van Dyke, briefly making Nance his son-in-law.
Nance was born in Boston, Massachusetts and was raised in Dallas, Texas. He graduated from South Oak Cliff High School. His father retired from Neiman Marcus. He worked for some time with the American Conservatory Theater in San Francisco. In the 1970s, Nance met David Lynch, who cast him as the lead in Eraserhead.
He was known for his work with Director David Lynch, particularly for his starring roles in Eraserhead (1977) and Twin Peaks (1990–1991).
Van Dyke committed suicide on November 17, 1991. According to her younger brother Richard, Nance, who was in Bass Lake, California, filming Meatballs 4 at the time, attempted to console her on the phone as she threatened suicide. After a lightning storm knocked out the phones in Bass Lake, Nance and the Director, Bobby Logan, found a deputy sheriff who contacted Los Angeles police and the apartment manager. They broke in and found that she had hanged herself.
Nance also guest-starred on a 1995 episode of My So-Called Life entitled "Weekend", in which he played an innkeeper. He also appeared with Actress Mary Woronov in Suicidal Tendencies' 1983 "Institutionalized" music video.
Nance died in South Pasadena, California, on December 30, 1996, under mysterious circumstances. On December 29, he lunched with friends Leo Bulgarini and Catherine Case. Nance had a visible "crescent shaped bruise" under his eye; and, when asked about it, he related to them the story about a brawl outside a Winchell's Donuts store on the morning of December 29. He described the incident as, "I told off some kid. I guess I got what I deserved." He soon went home, complaining of a headache.
The Nance tribute song "I Gotta Move" by Frank Black and the Catholics on their 1997 eponymous debut album refers to the circumstances of Nance's death.
A documentary about Nance funded by Lynch, titled I Don't Know Jack, was released in 2002.