Marshall was born in Owatonna, Minnesota, the son of Hazel Irene (née Cobb; 1892–1975) and Charles G. Grunz (1882–1959). His paternal grandparents were German. During his life, he chose not to reveal what "E. G." stood for, telling most people it stood for "Everybody's Guess," but it can be observed the initials match Everett (or Eugene) Grunz. According to the Social Security Death Index, his Social Security card showed his full name as: "E G Marshall". He attended both Carleton College and the University of Minnesota.
Although most familiar for his later television and movie roles, Marshall also had a distinguished Broadway career. In 1948, having already appeared in the original New York productions of The Skin of Our Teeth and The Iceman Cometh, Marshall would join Marlon Brando, Montgomery Clift, Julie Harris, Kim Stanley, and 45 others to make up the first group of actors granted membership in the newly formed Actors Studio. In subsequent years, he'd land the leading roles in The Crucible and Waiting for Godot. In 1973, he returned to the live stage to play the title role in a highly praised production of Macbeth in Richmond, Virginia, under the direction of Keith Fowler. From January 1974 until February 1982, Marshall was an occasional participant and the original host of the popular nightly radio drama, The CBS Radio Mystery Theater.
As a member of the Committee for National Health Insurance, Marshall was a long-time advocate of government-provided health care in the United States. During the 1968 United States presidential campaign, he filmed and narrated a political advertisement endorsing Democratic candidate Hubert Humphrey.
He died of lung cancer in Bedford, New York, on August 24, 1998. His grave is in the Middle Patent Rural Cemetery, located in the hamlet of Banksville, a part of the town of North Castle, New York.