Crenna was born November 30, 1926, in Los Angeles, the only child of Edith J. (née Pollette), who was a hotel manager in Los Angeles, and Dominick Anthony Crenna, a pharmacist. His parents were both of Italian descent. Crenna attended Virgil Junior High School, followed by Belmont High School in Los Angeles, from which he graduated in 1944.

Crenna got his acting start on radio. In 1937, he had gained his first role that of "the kid who did everything wrong" on Boy Scout Jamboree, a show on which he continued to appear occasionally in numerous roles until 1948. In the following year, he started playing Walter "Bronco" Thompson on The Great Gildersleeve, and played it until the show's end in 1957. He appeared as a delivery boy in My Favorite Husband episode "Liz Cooks Dinner for 12", was Oogie Pringle on A Date With Judy episode "The Competitive Diet" and several other episodes from the show and as a teenager on The George Burns and Gracie Allen Show episode "Watching the Neighbor's Daughter".

Following high school, Crenna served in the U.S. Army during World War II, serving in the infantry as a radioman, where he saw combat in Belgium during the Battle of the Bulge (late 1944–early 1945). He also briefly served in the Pacific Theater of World War II processing intercepted Japanese radio messages.

From 1948, Crenna played Walter Denton on radio's Our Miss Brooks remaining with the cast when it moved into television in 1952. He guest starred on the I Love Lucy episode "The Young Fans" with Janet Waldo and on NBC's 1955–56 anthology series, Frontier, in the lead role of the episode entitled "The Ten Days of John Leslie". In 1955, he was the guest star on The Millionaire in the episode "The Ralph McKnight Story".

In 1956 when the Our Miss Brooks TV series underwent a change in format, the character of Walter Denton was dropped. Crenna then joined the cast of the comedy series The Real McCoys, as Luke McCoy. Kathleen Nolan was cast as his young wife, Kate McCoy. Later, Crenna became one of the four Directors of the series during its six-year run (1957–63).

In the 1960s, Richard Crenna directed many episodes of The Andy Griffith Show credited as "Dick Crenna". He also directed episodes of Lou Grant, which ran on CBS from 1977-82.

Crenna portrayed California state senator James Slattery in the CBS-TV series, Slattery's People (1964–65). For his acting in this series, he was twice nominated for an Emmy Award with slightly different names: for "Outstanding Individual Achievements in Entertainment" and for "Outstanding Continued Performance by an Actor in a Leading Role in a Dramatic Series", both in 1965. Crenna was also nominated for a Golden Globe Award for "Best TV Star – Male" for this same role, again in 1965. In 1966, Crenna played beside Steve McQueen as an ill-fated captain of an American gunboat in 1930s China in The Sand Pebbles.

During the 1970s, Crenna continued his acting in such Western dramas such as Catlow, Breakheart Pass, and The Man Called Noon. He made a notable performance in Jean-Pierre Melville's final film Un Flic in 1972. In 1976 Crenna returned to weekly network television in the Norman Lear CBS sit-com All's Fair. The single season political satire co-starred a young Bernadette Peters. The 1978 NBC-TV miniseries, Centennial, based on James A. Michener's historical novel Centennial, saw Crenna in the role of deranged religious fanatic, Colonel Frank Skimmerhorn, who ordered the 1864 massacre of Colorado American Indians.

Crenna won an Emmy Award, and a nomination for a Golden Globe Award for Best Performance by an Actor in a Mini-Series or Motion Picture Made for Television, for his performance as the main character in the 1985 movie The Rape of Richard Beck.

Crenna played John Rambo's ex-commanding officer Colonel Sam Trautman in the first three Rambo films, a role for which he was hired after the actor Kirk Douglas left the production just one day into the filming of the first movie of the series. Crenna himself also spoofed this character in the movie Hot Shots! Part Deux, in 1993. Crenna portrayed the character of New York City Police Lieutenant of Detectives Frank Janek in a series of seven popular made for television films starting in 1988 and ending in 1994. The character of Janek originally appeared in a series of novels by Award-winning author william Bayer.

Crenna had pancreatic cancer, and died on January 17, 2003 at age 76 of heart failure at Cedars-Sinai Medical Center, with his wife, Penni, and his three adult children by his side, said his daughter Seana Crenna. His remains were cremated.