Recently, Los Angeles-based comedian Todd Glass decided to appear on the podcast hosted by fellow comic Marc Maron—and hilarity did not ensue.

When Mr. Glass first appeared on Mr. Maron’s show, WTF, in 2009, the program, in which Mr. Maron, the alt-comedy fixture and former Air America host known for his sometimes lacerating, self-exposing rants, was in its early days, and Mr. Glass did a little riff on “technophobia”—a fairly typical, if amusingly delivered, comedic bit.

By January 2012, however, Mr. Glass had a weightier issue to get off his chest—and the podcast was ready to accommodate him. Slowly, over the course of the episode, he came out of the closet. As fans heard the interview on iTunes or apps like Stitcher Smart Radio, the episode caught fire within the comedy community, not least because it came in the form of an extensive Socratic dialogue as opposed to a press release to Out or a quick-hit on late-night talk.

Longtime listeners of WTF are accustomed to hearing revealing conversations with figures they recognize from TV or local comedy clubs (or not at all), but for the uninitiated, Mr. Glass’s description of his vacillation over whether to reveal his sexuality, his anger at antigay rhetoric and the fear and anxiety he experienced throughout his life was exhilarating. “I didn’t get one piece of negative feedback—not even a Bible verse,” said Mr. Glass of the torrent of warm vibes listeners sent his way. For both its intimacy and its inside-baseball focus, his coming-out was a conversation that could have happened only on a podcast.

Asked why he’d chosen the forum for his big reveal, Mr. Glass noted that a bigger venue—David Letterman’s show, for instance—wouldn’t have had the kind of time to really explore the issue, whereas on WTF, “I knew we’d have an hour and a half. And I wanted it to be this person who could lead me down the path comfortably.” Mr. Glass and Mr. Maron had been casual friends for decades. “Some people have jokingly or seriously said he’s our version of Oprah today,” Mr. Glass noted. “You get into the atmosphere there and you’re comfortable.”

Mr. Glass isn’t joking. Anyone who believes a comedian as successful as, say, Louis C.K. is imperviously sardonic hasn’t heard him crying over his daughter’s birth on WTF. Mr. Maron, through his twice-weekly interview series, may have drawn more tears than any interviewer since Barbara Walters. “It’s like going on Dick Cavett,” said the comedian and podcast host John Hodgman. “It’s a sign of being taken seriously.”

The show is also, at least in part, responsible for kicking off a movement. Akin to the comedy-club boom of the 1980s, in which every city got its Chuckle Hut, comedy has suddenly become vastly more accessible—or at least, comedians have. Podcasts have given standups a powerful new platform that few seem able to resist. Even Mr. Glass recently started his own show.

Unlike Mr. Maron’s show, Mr. Glass’s is oriented toward humorous chat—basically. “Onstage, you have to be funnier than you are preachy,” he said. “That’s the overall rule in standup. People take a journey with you when you podcast.” (It’s not a short journey, either—Mr. Glass’s weekly show can run to two and a half hours.)

“I can be silly, we can go off on a tangent and be quite serious,” he explained. “The format for podcasts is: do whatever you fucking want.”

Mr. Maron felt little of the joy of experimentation when he first began podcasting. “I sort of came to it through desperation,” he said. “I was in a difficult place, career-wise and financially. I was running out of ideas and options. Jimmy Pardo was doing one and Kevin Smith was doing one. But I didn’t really know much about the medium.”

Episode one of WTF aired in September 2009. After Air America Radio shut down a few months later (“They’d run out of money for the fourth or fifth time, or whatever”), Mr. Maron kept his office security card and snuck into the studio to tape his own show. “We were taking guests up the freight elevator,” he said. These days, having long since ponied up for broadcast mics and an analog mixer, he records using the program GarageBand—in his garage.

“It’s the Wild West, it’s a tabula rasa,” Mr. Maron said.

“Marc only makes legendary episodes,” said Mr. Hodgman. “Marc is an exemplar of the form in the sense that this low-barrier-to-entry broadcast format gives voice not just to a lot of people in the comedy field but to the different kinds of voices and skills comedians can use.”