Allan was married to Toby Brown from September 21, 1958 until her death in 2001. The couple had three sons, Mitch, Dean, and Rick. Allan lives in Palm Desert, California.

Allan has starred in several soap operas. He made his debut as trouble-making Ace Hubbard on Love of Life in 1964. From 1964-65, he was one of many actors to play college professor Paul Britton on The Secret Storm who was involved with the show's leading heroine, Amy Ames. Allan replaced his Future Santa Barbara co-star Nicolas Coster in the part. He may be best known for his role as Don Craig in Days of Our Lives, which he played from 1971 to 1985, his exit taking place as many of the show's veteran cast members were being written out so the show could focus on younger characters. In 1973 Allan was a featured character in an episode of Adam-12 titled "Capture." His departure from Days of our Lives was controversial, as his character was abruptly written out with no further explanation. He gained a new audience when he took over the role of C.C. Capwell in Santa Barbara from 1986 to 1993. After his time on Santa Barbara, Allan had a recurring role in Beverly Hills, 90210 playing Rush Sanders.

Allan's most notable TV role outside of soap operas was when he starred on Lassie from 1968–70 as Forest Ranger Scott Turner, who (along with another ranger) served as the iconic collie's main human companion during that time frame. He was a pitchman in commercial spots in 1980-1981 for McDade's, a local catalog department store chain in the Chicago area, as well as for Two Guys Department stores.

Allan has appeared in numerous made for TV movies, hosted Celebrity Bowling during the 1970s, and wrote a book, Please, Spell the Name Right, in reference to his name often being spelled incorrectly. The book is about his experiences of 50 years as an actor working with other actors and was released in November 2004. He also hosted a game show pilot, Temptation, in 1981 for Ralph Andrews and Columbia Pictures Television.

In 2004, he started playing the role of Edward Quartermaine in General Hospital. This was in some ways unusual casting, as the actor who played Edward's son Alan, Stuart Damon, is a month older than Allan himself. Prior to starring on General Hospital he starred in its spinoff Port Charles. In 2006, it was announced that John Ingle, the actor who had played Edward before Allan, was returning, and Allan would relinquish the role. Ingle returned to the role in spring 2006.