He made his film debut in 1951 with a small role in MGM's Teresa, followed by a starring role in the Swiss-made Four in a Jeep, directed by Leopold Lindtberg.
For his performance in the play Picnic, Meeker was awarded the New York Critic's Circle Award in 1954. Picnic became a classic film in 1956, with William Holden and Kim Novak starring in the roles originated by Meeker and Janice Rule.
Meeker starred as Mike Hammer in the 1955 Robert Aldrich film of Mickey Spillane's Kiss Me Deadly. In 1957 he co-starred in Stanley Kubrick's Paths of Glory, playing one of the condemned soldiers. He also played George "Bugs" Moran in the film St. Valentine's Day Massacre (1967). That same year, he appeared as Captain Stuart Kinder, the military psychologist who attempts to analyse the Dirty Dozen. He played the police captain in The Anderson Tapes (1970).
He was the producer of the movie My Boys Are Good Boys (1978) and made guest appearances on numerous TV shows, including Ironside, CHiPs, Toast of the Town, Outer Limits and Studio One.
He was a graduate of the Leelanau School in Glen Arbor Township, Michigan, and a member of their Hall of Fame. Meeker married two times. His first wife was actress Salome Jens. The marriage lasted from 1964 to 1966. His second marriage was to Colleen Meeker. Major success continually eluded him. He died of a heart attack on August 5, 1988, in Woodland Hills, California.
