Cullen was born in Pittsburgh, Pennsylvania, and survived a childhood bout with polio that left him with a limp for the rest of his life. (In most of his later game shows, the set was designed in such a way that he came out from behind the curtain or from off stage riding on something of a turntable so that he never had to walk any distance across the stage and advertise this fact.) Unlike the typical appearance-conscious television personality, he also wore very thick glasses, which became kind of a trademark.

After moving to New York City he hosted several radio programs, including game shows, in the late 1940s and 1950s. His first TV game show was Winner Take All, a Mark Goodson-Bill Todman production that aired on CBS in 1952. He hosted the highly successful daytime and prime-time versions of The Price is Right, another Goodson-Todman production, from 1956 to 1965. He was also a panelist on I've Got a Secret from 1952 until 1967 and then on To Tell the Truth from 1969 until 1978, where he would also guest host on occasion.

Cullen hosted 20 different game shows over the years, including Eye Guess in the 1960s, Three on a Match and the nighttime version of The $25,000 Pyramid in the 1970s, and Blockbusters, Child's Play, Hot Potato, and The Joker's Wild (his last game show) in the 1980s. He appeared as a celebrity guest on many other game shows throughout his TV career, including I've Got a Secret, Password, To Tell the Truth, Match Game, and the daytime versions of Pyramid that Dick Clark hosted.

He became a favorite of TV producers for his seeming unflappability in live television moments. Quiz-show creator and close friend Bob Stewart enlisted him for multiple pilots and series. To this day he is the only person who's hosted the top four Stewart-created games on a full- or part-time basis -- The Price Is Right, To Tell the Truth and Password (as Password Plus, during Allen Ludden's illness) for Goodson-Todman Productions, and the 1970s nighttime Pyramid for Bob Stewart Productions. He also emceed Stewart's first national game show as an independent producer, the 1966-69 show Eye Guess.

He was a pilot during World War II and had a long time love of anything mechanical. He did color commentary on college football games early in his career, and was even once involved in the broadcasting of track and field on NBC. On I've Got A Secret especially, the producers learned early on that if they wanted to keep the game going for a while, they would never start with Bill if it was anything sports-related or mechanical, because chances were good that he would nail it immediately.

Cullen was married three times. His first marriage was a brief one while still living in Pittsburgh. His second marriage was to singer Carol Ames from 1949 to 1955. He was then married to former dancer and model Ann Macomber from 1955 until his death in 1990 from lung cancer at the age of 70, after having been a smoker for all of his adult life.