Like other 20-somethings seeking a career foothold, Andrew Lang, a graduate of Penn State, took an internship at an upstart Beverly Hills production company at age 29 as a way of breaking into movie production. It didn’t pay, but he hoped the exposure would open doors.

When that internship proved to be a dead end, Mr. Lang went to work at a second production company, again as an unpaid intern. When that went nowhere, he left for another, doing whatever was asked, like delivering bottles of wine to 27 offices before Christmas. But that company, too, could not afford to hire him, even part time.

A year later, Mr. Lang is on his fourth internship, this time for a company that produces reality TV shows. While this internship at least pays him (he makes $10 an hour, with few perks), Mr. Lang feels no closer to a real job and worries about being an intern forever. “No one hires interns,” said Mr. Lang, who sees himself as part of a “revolving class of people” who can’t break free of the intern cycle. “Is this any way to live?”

The intern glass ceiling isn’t limited to Hollywood. Tenneh Ogbemudia, 23, who aspires to be a record executive, has had four internships at various New York media companies, including Source magazine and Universal Music Group.