Julia Roberts is an icon of the romantic-comedy genre, but there’s one famous rom-com the Oscar-winner happened to turn down: Nora Ephron’s 1998 classic “You’ve Got Mail.” Roberts revealed the scoop during a recent appearance on Bravo’s “Watch What Happens Live.”

Ephron’s film memorably paired Tom Hanks and Meg Ryan in the story of business rivals unaware they are falling in love with each other online. “You’ve Got Mail” marked the third Hanks-Ryan romantic comedy after “Joe Versus the Volcano” (1990) and “Sleepless in Seattle” (1993), the latter title also being directed by Ephron. Had Roberts taken the role, it would’ve extended her 1990s rom-com streak that already included hits like “Pretty Woman” (1990), “Notting Hill” (1999) and “My Best Friend’s Wedding” (1997).

Asked by a fan to name some roles she has turned down in career, Roberts stressed that she does not regret any of her choices. She said any...