But now, Cage, who chewed a cockroach in Vampire's Kiss (1989) and played a reckless misfit in David Lynch's Wild at Heart (1990), is making a startling career turnaround.
It began with the 1993 film Honeymoon in Vegas in which Cage took his first stab at becoming a conventional leading man. The trend continues with Guarding Tess, a comedy in which he portrays a straight-arrow Secret Service agent assigned to protect a former first lady (Shirley MacLaine). The film is scheduled to open nationwide on Friday.
Sitting in a Manhattan hotel room, wearing a simply cut black jacket and white shirt, Cage looks disarmingly normal. Yet there's still something
intriguingly off-center about the grin he flashes as he talks about his determined plunge into the Hollywood mainstream.
"Actually, I guess I was a little nervous about becoming so straight on the screen because I was worried about whether I would still be interesting," he says. "I knew I had an affinity for crazy kinds of roles and I wondered about whether I could do more ordinary people."
Doug Chesnic, the Secret Service agent who is forced by ex-first lady Tess Carlisle to become a de facto servant, is probably the most conventional character Cage has played.
"What's humorous about Doug," Cage says, "is how seriously he takes his job, considering how demeaning it really is. He's essentially a gofer with a gun.
"I mean, when he's in a supermarket with Tess he's getting price checks on the canned peas and handling it like it's Mission Impossible. Doug is a completely dedicated straight kind of guy."
Chesnic's penchant for going by the book is seriously challenged by Tess. The two become locked in a hilarious contest of one-upmanship, with Tess apparently determined to see just how many of Chesnic's buttons she can push.
Along with the other agents assigned to Tess, Chesnic is forced to cater to such whims as a round of golf on the local course in the dead of winter.
While doing research for the film, Cage discovered that this crotchety, strong-willed former first lady character was more than a product of writer- director Hugh Wilson's imagination.
"I spoke with Secret Service agents assigned to wives of ex-presidents who've been called on to do some odd things," the actor says.
"I remember one told me about having to cook corned-beef stew for, I believe, Mamie Eisenhower. This guy had never even heard of corned-beef stew, but he cooked it anyway.
"Actually, I think Tess is a composite of a lot of former first ladies, with quite a bit of Bess Truman in there."
For Cage, the thought of working with MacLaine was almost as intimidating as the idea of being assigned to guard a famous political figure.
"I was very nervous to meet her, because I was a huge fan of hers," admits Cage, whose best-known role was as Cher's opera-loving misfit - there's that word again - suitor in Moonstruck (1987). "Shirley is a legend, and I'd never worked with a legend before."
With a laugh, Cage says that MacLaine more than exceeded his expectations.
"She's a super-pro, but she also has this tough side and, like Tess, she can unleash some very sharp-edged repartee which keeps you fighting to hold your own," Cage says.
"I was talking to her about the love affair she had with Robert Mitchum," Cage says. "He was always one of my favorite actors, so I asked her what he was really like.
"And she said, 'Oh, I just loved Bob's big body. He's kind of like Bill Clinton, you know, those same broad shoulders.'
"Then she said, 'You know, Nick, you're not my type. You work out too much. You're too skinny. You need to gain some weight.'
"It was all in fun," he says, smiling.
Still, Cage had a good time making Guarding Tess and says he hopes to do more films in the same vein.
"I've decided that people respond better to me in comedies than all that quirky stuff I did in the past," he says.
"It's funny, when I was a kid I used to like to make people laugh. I was in a very tough school and it became sort of a survival mechanism for me. But then I saw James Dean in East of Eden and I decided I wanted to be like him.
"I made a lot of angst-ridden pictures and found myself approaching bankruptcy. So I decided to go back to what came naturally to me - being funny rather than unconventional."
Born Nicolas Coppola, the youngest of three brothers, Cage grew up in Long Beach, Calif.
His childhood was pretty conventional, except for the fact that his uncle, Francis Ford Coppola, was a famous film director. That came in handy when young Nick decided to pursue an acting career. In fact, Cage made his film debut in Coppola's Rumble Fish (1983).
But he quickly discovered that having an uncle in the business also had a downside: It made people skeptical about whether he could make it on his own.
So Nicolas changed his last name to Cage, and happily found that he had no trouble landing roles. He soon had Hollywood talking about his performances as the disfigured Vietnam vet in Birdy (1984) and the baby-snatcher in Raising Arizona (1987).
"I think that angst, that drive I had in those days was fueled by a lot of inner anger, a sort of rebel rage," Cage says.
"My heroes were groups like The Who. I really liked the idea of having that outlaw image, that rock-and-roll persona, that edge of being a wild man."
Cage shakes his head at the memory.
"I'm 30 now," he says. "People change as they get older. I sometimes wonder if I can still call back that intensity, that drive."
A major factor in the mellowing of Nicolas Cage has been parenthood. Cage admits that he has become preoccupied with being a father to his 3-year-old son, Weston, whose mother is model Christina Fulton.
Although unmarried, and living apart, the couple share child-rearing duties.
"I worry a lot about him," Cage says of his son. "In fact, I couldn't go see Robert Altman's Short Cuts because I know a little boy gets hit by a car and eventually dies. I just knew I wouldn't be able to watch that scene. I knew it would make me worry more than I already do."
The actor also worries about combining the demands of his career with the demands of parenthood.
"It's a double-edged sword," he says with a sigh. "When Weston was born I almost instinctively clicked into a kind of overdrive. I was saying to myself, 'I have a responsibility. I've got to go to work. I've got to provide.'
"But then I feel guilty because when I'm making a film I'm not with him as much as I'd like to be. "
Though fatherhood has definitely had a mellowing effect on Cage, one example of his former affection for the bizarre stays with him: the large tattoo of a lizard - complete with a top hat and cane - on his back.
"When I got that I really needed to claim my own body," Cage says. "I know that sounds way out, but it's true. Other cultures have initiations into manhood and that's what the tattoo was for me.
"I think it all came together for me when my father first saw it. I'll never forget the look on his face. He turned white. I said, 'Dad, guess what? I'm my own man now.' "
And how does Weston feel about Daddy's tattoo?
"Well, he does notice it," Cage says, "but he hasn't said anything about it yet. I do notice that he's been playing with some of those press-on tattoos, though."
Suddenly Cage erupts into laughter.
"You know what? If Weston ever came home with a lizard tattoo on his back, I'm not sure I could deal with it. I don't think I'll ever let him get away with that."