His credits include roles in Oscar winner The Social Network, and teen smash American Pie. He's been directed by Spielberg in Catch Me If You Can and, as a regular on Glee, you might expect actor Jesse Heiman to be the most recognisable face in Hollywood. But Jesse is a "background actor", one of the legions of performers paid a minimum wage to lurk in the background of some of cinema's biggest films. Despite their efforts they remain anonymous, and that was Jesse's fate too until a compilation of his remarkable 11-year screen career racked up more than 1m views on YouTube.

"People keep asking me, 'Have you seen this video?'" laughs Jesse, incredulously. "Seen it? I've lived it!" Giving his first ever interview, Jesse, 32, sips a coffee outside a small cafe on Hollywood Boulevard, a baffled agent in tow. "It was the number one, number six and number eight top videos watched in Sweden last week." He shrugs: "The phone hasn't stopped ringing."

Set to the rousing score from Requiem For A Dream, the two-minute montage is introduced with the words: "Do you recognise this brilliant actor? According to the myth he appears in every movie and TV show ever created. I found a few of them." While the claim may not be quite true, the portly Bostonian has made a staggering 56 appearances in mainstream movies and television shows since his 2001 debut as Petey, the unnoticeable trombone player American Pie 2. He is officially the most ubiquitous actor in Hollywood.

On graduating from Texas State University in 2000, Jesse surprised friends with a move to Los Angeles to embark on an acting career. After American Pie 2, he reprised his role as an awkward-looking student in the college romp Van Wilder, but in 2002, he would get his biggest break, peering over Kirsten Dunst's shoulder in Spider-Man. Next, drive-by appearances followed on the smaller screen, in shows such as Entourage, The OC, Arrested Development, and a blink-and-you-missed-it spot on My Name Is Earl.

'Steven Spielberg is a master of setting the scene. Every actor, every prop is vital. He gave me some personal direction'

Heiman's the man: Jesse (right) in Catch Me If You Can

"Did you see Catch Me If You Can?" Jesse asks excitedly. "Spielberg is my hero. The reason I got into acting. He directed me on Catch," he sighs, as casually as Harrison Ford might talk about Raiders. "It was one of the best moments of my life." Jesse recalls the long day he spent on set, in a classroom scene where DiCaprio's character Frank Abagnale Jr narrowly escapes capture. "Leo came up and said 'hello' before the take," he recalls, "and Spielberg is a master of setting the scene. Every actor, every prop is vital. Then Spielberg gave me some personal direction." Jesse pauses before impersonating the great auteur: "'Can you put your face more into the book, please?'"

"On The Social Network I worked 13 hours, through the night until 4am, it was exhausting," Jesse continues. "We shot it at the University of Southern California, and we had to shoot at night because the college was in session, and that was only for a short scene." Of director David Fincher, Jesse says: "He's a very serious guy, a genius. It took a few takes but he happened to put me in a great spot. I have a great track record with big directors; they always want to put me right centre."

It is true that directors seek Jesse out; Michael Bay hand-picked him for two of his Transformers films. But the suspicion remains that casting Jesse over and over is one big industry joke. And if so, the actor isn't in on it.

In fact, Jesse has his sights set on moving from background to foreground. "I'm a character actor," he insists. "I think I could become one of the great character actors like Jonah Hill." The physical similarity is undeniable, but the two performers are far from friends. "I think I'm nicer than Jonah. I've met him, he's a bit of a ... well, let's not go there. I don't think he respects background actors," he whispers, flushing crimson. "I prefer to think of myself as more like a John Candy kind of actor, anyway. If there's ever a Planes, Trains & Automobiles reboot or remake I could see myself in that."

Most extras will tell you that Tom Cruise, Brad Pitt and Eva Longoria all got their showbiz starts in uncredited roles. But despite the apparent success, Jesse is still waiting for the big bucks. "Over time you can make money, but I don't get any residuals," Jesse explains. "I get a base rate for a Screen Actors Guild union actor. Extra work is $139 [£86] for eight hours' work, plus there are meal penalties and transportation allowances." With that, Jesse insists on paying for the Guardian's coffee, slips his shades on and heads back to his modest apartment in Studio City.

"You know Jonah Hill's already made millions of dollars, but that's not my life yet," he says. "I'm just praying for a speaking role."