Allen was born in Mount Vernon, New York and graduated from the New York Military Academy in 1924, where he rode in the academy cavalry and from Dartmouth College in 1929 with a degree in English. In vacations he had driven a truck as a labourer. He worked for a bank which soon failed in the Great Depression. He flew briefly with the Curtis Flying service as a commercial pilot. He first came to the screen in 1926 before signing a standard acting contract with Paramount Pictures, in 1929. He appeared in the Marx Brothers movie Animal Crackers and several other small parts. Then, he signed with Columbia Pictures in 1935. He also later contracted with 20th Century Fox. Allen's first notable role was the male lead in Love Me Forever, for which he won a Box Office Award. After the departure of cowboy star Ken Maynard, Allen was plugged into producer Larry Darmour's formulaic Ranger pictures. Along with sidekick Wally Wales, he redefined the role, starring in six films for director Spencer Gordon Bennet in that year alone. The star was billed as Bob Allen. However, the great success of Wild Bill Elliott in Columbia's 1938 serial The Adventures of Wild Bill Hickok prompted Columbia to drop Bob Allen and replace him with Elliott. Allen continued to work in pictures, as Robert Allen or Robert "Tex" Allen. He had acted on Broadway in the original productions of Show Boat and Kiss Them for Me. In 1956 he appeared in the original production of Auntie Mame, opposite Rosalind Russell, and later Greer Garson. He appeared in other Broadway plays, in touring productions, in soap operas, documentaries and commercials. He became a real estate broker in 1964 but returned to the stage from time to time, including an appearance as J.B. Biggley in the 1972 Equity Library Theatre revival of How to Succeed in Business Without Really Trying.
Family
Allen was married twice; the first was to movie actress Evelyn Peirce until her death in 1960. They had two children. Their son, Ted Baehr is a prominent Christian minister and movie critic. They also had a daughter, Katherine Meyer. Allen died on October 9, 1998, aged 92, of complications from cancer in Oyster Bay, Long Island, New York. He was survived by his son and daughter, seven grandchildren and eight great-grandchildren.