Blyden was born to Adolph and Marian (née Davidson) Blieden in Houston, Texas, and raised in the Jewish faith. As a child, he attended Wharton Elementary School and Sidney Lanier Junior High School. Blyden became interested in acting at a young age and made his stage debut in a production headed by Margo Jones when he was 14 years old. After graduating from Lamar High School, Blyden attended Southwestern Louisiana Institute for a year before enlisting in the United States Marine Corps during World War II. After the war, he enrolled at the University of Houston. While in college, Blyden worked as an announcer for KPRC radio and performed at the Alley Theatre and Houston Little Theater. After graduating with a Bachelor of Arts in 1948, Blyden moved to New York City to pursue an acting career.

While in New York, Blyden again worked in radio and studied acting at the Stella Adler Studio of Acting for eighteen months. While starring in a showcase of The Importance of Being Earnest, he was spotted by Director Joshua Logan who cast him in a small role in the Broadway production of Mister Roberts. He was then cast in the larger role of "Ensign Pulver", and remained with the production until 1951. His second Broadway role was that of "Schmutz" in the original production of Wish You Wish Here. In 1958, Blyden replaced Larry Storch as "Sammy Fong" in the out-of-town tryouts for the musical Flower Drum Song. He remained in the role during the show's original Broadway run for which he was nominated for a Tony Award for Best Actor in a Musical. The show was choreographed by his then-wife, Carol Haney. That same year, he appeared in You Can't Take It with You, at Expo 58 (also known as Brussels World's Fair).

Blyden married Actress and Dancer Carol Haney on April 17, 1955 in Las Vegas. The couple had two children: Joshua and Ellen Rachel. Blyden and Haney were divorced in 1962.

Over the course of his career, Blyden appeared in three feature films. He made his film debut in a supporting role in the 1957 drama The Bachelor Party, starring Don Murray. He also had supporting roles in Kiss Them for Me (1957) and On a Clear Day You Can See Forever (1970).

After the cancellation of Joe and Mabel, Blyden returned to stage work (replacing Ray Walston in the Philadelphia and Broadway runs of Who Was That Lady I Saw You With? and Flower Drum Song). He returned to television in 1959 as "Sammy Glick" in the television adaptation of Budd Schulberg's 1941 novel What Makes Sammy Run?. The two-part special aired on the NBC Sunday Showcase on September 27 and October 4, 1959, and also starred John Forsythe, Dina Merrill and Barbara Rush.

In the late 1960s, Blyden began working as a game show host and master of ceremonies starting with Personality in June 1967. In 1969, he hosted You're Putting Me On and The Movie Game. In 1972, Blyden took over hosting duties for the syndicated revival of the game show What's My Line?. Blyden remained the show's host until it was canceled in 1975.

During their marriage, Blyden and Haney purchased the historic Achenbach House in Saddle River, New Jersey, which they believed to be haunted by the spirit of its builder. After Haney's death in 1964, Blyden inherited the home and became convinced that her spirit was haunting the house. Blyden later told a friend that in the months after Haney's death, the house was filled with the smell of brownies baking which had been Haney's favorite. Blyden told his friend that after he yelled at Haney to leave him alone, the smell instantly vanished. The house was later sold to tour operator Mario Perillo and was destroyed by fire in 2004.

In November 1962, Blyden tried his hand at stage directing in the Broadway production of Harold, starring Anthony Perkins and Don Adams. The production closed after twenty performances. In February 1967, Blyden replaced Martin Balsam in the Broadway production of You Know I Can't Hear You When the Water's Running. Blyden's second stage directing effort was the play The Mother Lover, in which he also starred. The production also featured Eileen Heckart and Valerie French and premiered at the Booth Theatre on February 1, 1969. In March 1972, he portrayed the role of "Hysterirum" in the revival of A Funny Thing Happened on the Way to the Forum, starring Phil Silvers, which Blyden also produced. He won the Tony Award for Best Featured Actor in a Musical for his work in the play.

In 1974, Blyden appeared as "Dionysos" with the Yale Repertory Theatre in the musical comedy The Frogs, in New Haven, Connecticut. The play was written by Burt Shevelove, and based on a play written by Aristophanes in 405 B.C. The play's music and lyrics were composed by Stephen Sondheim. Blyden's final stage role was that of "Sidney" in Alan Ayckbourn's comedy Absurd Person Singular, for which he was nominated for a Drama Desk Award for Outstanding Featured Actor in a Play and a Tony Award for Best Actor in a Play. He remained with the production for 250 performances.

On May 6, 1975, Blyden left the production of Absurd Person Singular after he was hired to host a new game show entitled Showoffs. He videotaped the pilot episode on May 24. Before production was set to begin, Blyden was granted a two-week vacation and decided to fly to Marrakesh, Morocco. While driving near Agadir on May 31, Blyden's rental car reportedly went off the road and overturned. According to Blyden's manager, Blyden suffered injuries to the chest, head and abdomen. He underwent surgery but died of his injuries on June 6. Blyden's body was flown back to the United States on June 13. A memorial was held on June 20 after which he was buried at Forest Park Lawndale Cemetery in Houston. His death came 17 days before his 50th birthday.

Mark Goodson, the Producer of Showoffs, later told Variety that he felt the circumstances leading to Blyden's death were unclear. Goodson said that his production company, Goodson–Todman Productions, was initially informed that Blyden had been involved in a car accident while driving to Marrakesh and was hospitalized with serious injuries. A second report from the American consulate claimed that Blyden's injuries were not serious and only required minor surgery. A few days later, it was announced that Blyden was dead. On the audio commentary for the 2009 DVD of What Makes Sammy Run?, Blyden's co-star Barbara Rush claimed that Blyden had been carjacked by bandits and killed.