Film

Roberts collaborated with Woody Allen. In Annie Hall, he portrayed Alvy Singer's best friend Rob. Other Allen movies and plays in which he has appeared include both the Broadway and movie versions of Play It Again, Sam, Radio Days, Stardust Memories, Hannah and Her Sisters, A Midsummer Night's Sex Comedy, and Woody Allen's segment for The Concert for New York City.

Roberts portrayed Deputy Mayor Warren LaSalle in The Taking of Pelham One Two Three. He also appeared in the Sidney Lumet movies Serpico and Just Tell Me What You Want. Roberts was in the 1983 horror movie Amityville 3-D, portraying John Baxter.

Roberts was featured in 2014's The Longest Week.

Theater

Roberts's Broadway credits include Barefoot in the Park; How Now, Dow Jones; Murder at the Howard Johnson's; Promises, Promises; Sugar (the musical version of the movie Some Like It Hot); The Sisters Rosensweig; They're Playing Our Song; Victor/Victoria; The Tale of the Allergist's Wife; Arsenic and Old Lace; and Cabaret. In 1998, he played Buddy Plummer in Stephen Sondheim's Follies at the Paper Mill Playhouse in New Jersey. In 2007, Roberts returned to Broadway in the musical Xanadu.

Television and radio

For television, Roberts was the third actor to play Lee Pollock on The Edge of Night. He has appeared in numerous series such as The Carol Burnett Show, Matlock, and Law & Order. In 1977, he featured in the short-lived series Rosetti and Ryan with Squire Fridell.

In 1978, he was on The Love Boat. Roberts and Lauren Tewes's character, cruise ship director Julie McCoy, fall in love but don't pursue a relationship.

He featured (with Penny Fuller, who had played his wife on The Edge of Night) on the ABC comedy The Thorns. He was a regular performer on the CBS Radio Mystery Theater. Roberts also provides the narration on many of the audiobooks in Stuart Woods's Stone Barrington novels. Other audiobook credits include Andrew Vachss's Batman: The Ultimate Evil, Kurt Vonnegut's Cat's Cradle, and Spencer Johnson's Who Moved My Cheese?.