Born on Chicago's North Side to a middle-class Jewish family, Goodman began writing and performing songs as a teenager, after his family had moved to the near north suburbs. He graduated from Maine East High School in Park Ridge, Illinois in 1965. In the fall of 1965, He entered the University of Illinois and pledged Sigma Alpha Mu (Sammies) fraternity where he, Ron Banyon, and Steve Hartmann formed a popular rock cover band, "The Juicy Fruits". He left college after one year to pursue his musical career. In the early spring of 1967 Goodman went to New York, staying for a month in a Greenwich Village brownstone across the street from the Cafe Wha? where Goodman performed regularly during his brief stay there. Returning to Chicago he intended to restart his education but he dropped out again to pursue his musical dream full time after discovering the cause of his continuous fatigue was actually leukemia, the disease that would be present during the entirety of his recording career, until his death in 1984. In 1968 Goodman began performing at the Earl of Old Town in Chicago and attracted a following. By 1969, Goodman was a regular performer in Chicago, while attending Lake Forest College. During this time Goodman supported himself by singing advertising jingles.
In September 1969 he met Nancy Pruter, who was attending college while supporting herself as a waitress. They were married in February, 1970. Though he experienced periods of remission, Goodman never felt that he was living on anything other than borrowed time, and some critics, listeners and friends have said that his music reflects this sentiment
Goodman's songs first appeared on Gathering at The Earl of Old Town, an album produced by Chicago record company Dunwich in 1971. As a close friend of Earl Pionke, the owner of the folk music bar, Goodman performed at The Earl dozens of times, including customary New Year's Eve concerts. He also remained closely involved with Chicago's Old Town School of Folk Music, where he had met and mentored his good friend, John Prine.
Later in 1971, Goodman was playing at a Chicago bar called the Quiet Knight as the opening act for Kris Kristofferson. Kristofferson, impressed with Goodman, introduced him to Paul Anka, who brought Goodman to New York to record some demos. These resulted in Goodman signing a contract with Buddah Records.
All this time, Goodman had been busy writing many of his most enduring songs, and this avid songwriting would lead to an important break for him. While at the Quiet Knight, Goodman saw Arlo Guthrie, and asked to be allowed to play a song for him. Guthrie grudgingly agreed, on the condition that Goodman buy him a beer first; Guthrie would listen to Goodman for as long as it took Guthrie to drink the beer. Goodman played "City of New Orleans", (original lyrics) which Guthrie liked enough that he asked to record it. Guthrie's version of the song became a Top 20 hit in 1972, and provided Goodman with enough financial and artistic success to make his music a full-time career. The song, about the Illinois Central's City of New Orleans train, would become an American standard, covered by such musicians as Johnny Cash, Judy Collins, Chet Atkins and Willie Nelson, whose recorded version earned Goodman a posthumous Grammy Award for Best Country Song in 1985. A French translation of the song, "Salut Les Amoureux", was recorded by Joe Dassin in 1979. According to Goodman, the song was inspired by a train trip he and his wife took from Chicago to Mattoon, Illinois.
In 1974, singer David Allan Coe achieved considerable success on the country charts with Goodman's and John Prine's "You Never Even Called Me By My Name", a song which good-naturedly spoofed stereotypical country music lyrics. Prine refused to take a songwriter's credit of the song, although Goodman bought Prine a jukebox as a gift from his publishing royalties.
Goodman's success as a recording artist was more limited. Although he was known in folk circles as an excellent and influential songwriter, his albums received more critical than commercial success. Ironically, one of Goodman's biggest hits was a song he didn't write – "The Dutchman", written by Michael Peter Smith.
During the mid- and late-seventies, Goodman became a regular guest on Easter Day on Vin Scelsa’s radio show in New York City. Scelsa’s personal recordings of these sessions eventually led to an album of selections from these appearances, The Easter Tapes.
In 1977, Goodman performed on the Tom Paxton live album New Songs From the Briarpatch (Vanguard Records), which contained some of Paxton's topical songs of the 1970s, including "Talking Watergate" and "White Bones of Allende", as well as a song dedicated to Mississippi John Hurt entitled "Did You Hear John Hurt?"
Goodman wrote and performed many humorous songs about Chicago, including three about the Chicago Cubs: "A Dying Cub Fan's Last Request", "When the Cubs Go Marching In" and "Go, Cubs, Go" (which has frequently been played on Cubs' broadcasts and at Wrigley Field after Cubs wins.) He wrote "Go, Cubs, Go" out of spite after then GM Dallas Green called "A Dying Cub Fan's Last Request" too depressing. The Cubs songs grew out of his fanatical devotion to the team, which included many clubhouse and on-field visits with Cub players. He wrote Other songs about Chicago included "The Lincoln Park Pirates", about the notorious Lincoln Towing Service, and "Daley's Gone", about Mayor Richard J. Daley. Another comic highlight is "Vegematic", about a man who falls asleep while watching late-night TV and dreams he ordered many products that he saw on infomercials. He could also write serious songs, most notably "My Old Man", a tribute to Goodman's father, Bud Goodman, a used car salesman and World War II veteran.
On September 20, 1984, Goodman died of leukemia at the University of Washington Medical Center in Seattle, Washington. He had anointed himself with the tongue-in-cheek nickname “Cool Hand Leuk” (other nicknames included “Chicago Shorty” and “The Little Prince”) during his illness. He was 36.
Four days after Goodman's death, the Chicago Cubs clinched the Eastern Division title in the National League for the first time ever, earning them their first post-season appearance since 1945, three years before Goodman's birth. Eight days later, on October 2, the Cubs played their first post-season game since the 1945 World Series. Goodman had been asked to sing "The Star-Spangled Banner" before it; Jimmy Buffett filled in, and dedicated the song to Goodman.