[1] He won an Academy Award for Best Supporting Actor for his performance in the film Sweet Bird of Youth (1962) and appeared in such classics as 12 Angry Men (1957), Odds Against Tomorrow (1959) and The Unsinkable Molly Brown (1964).

[2][3][4] After he dropped out of school as a fifth-grader, Begley ran away from home several times, going to work for "carnivals, fairs, and small circuses".

He also starred in the 1950s radio program Richard Diamond, Private Detective, playing Lieutenant Walter Levinson, head of homicide at the 5th Precinct, Manhattan.

In 1954 Begley starred in the NBC Television show Robert Montgomery Presents in "Big Boy", an episode sponsored by Lucky Strike, as Joe Grant, an engineer for the Union Pacific Railroad living in Cheyenne, Wyoming, who worked on the famous Union Pacific Big Boy steam locomotives.

Some of his other notable films include Deadline – U.S.A. (1952), 12 Angry Men (1957) as juror #10, Odds Against Tomorrow (1959), The Unsinkable Molly Brown (1964), and Wild in the Streets (1968).

One notable role Begley played both on television (twice in 1955) and in the theatrical film (1956) is William (Bill) Briggs, one of the three primary characters in Rod Serling's Patterns.