After years of making movies that tickled his own fancy, Johnny Depp decided to do one for his kids. He figured his daughter Lily-Rose, 7, and son Jack, 4, would get a big kick out of Pirates of the Caribbean: The Curse of the Black Pearl. So he tied on the bandana, and went to work.

When the film opened in 2003, it wound up grossing $653 million at the box office and earned Depp a Best Actor Oscar nod. The world’s quirkiest leading man became, over the course of a single weekend, a bankable movie star.

In typical Depp fashion, there was nothing ordinary about the performance that transported him to A-list. The actor managed to twist a stock character—veteran pirate Capt. Jack Sparrow—into a woozy, gold-teeth wearing dandy. His inspiration, he noted famously at the time, was a cocktail of Keith Richards and cartoon skunk Pepe Le Pew.

So what, after all is said and done, did Depp’s kids think of their Daddy’s Pirates performance?

“They loved it,” Depp says proudly. “For a while there, my kiddies were watching Pirates I every single day. Then they moved on to Charlie and the Chocolate Factory. But now my son is into Spider-Man and things like that. They have to branch out, explore other worlds.”

The much-hyped sequel brings back most of the key players from the first film, including Orlando Bloom and Keira Knightley. So confident is Disney that the film will bring in plenty of box office booty that another sequel has already been shot and is scheduled to set sail next summer.

Depp had no qualms about returning for both sequels and hints he’d be willing to reprise Sparrow several more times. “Jack’s just a really fun character to play,” says the actor, 43. “I certainly wasn’t ready to say goodbye to him after the first film. I felt like there was a lot more to be done, a lot more fun to be had.”

This time around, the action begins with the arrest of Will (Bloom) and Elizabeth (Knightley) on charges of aiding and abetting Capt. Jack. In hopes of clearing his beloved, Will sets out to track down Jack and convince him to turn over a magical compass to power-mad baddie Lord Beckett (Tom Hollander.)

Jack, for his part, is hardly enjoying a day at the beach. As if owing his soul to Capt. Davy Jones (Bill Nighy) wasn’t bad enough, he finds himself on an island of cannibals who have made him their god, which is a mere prelude to turning him into their main course.

As helmed by returning director Gore Verbinski, Pirates 2 boasts a handful of attention-getting action scenes, including a sword fight staged on a huge water-mill wheel as it rolls down a hill, and a Sparrow-sliming interlude that boasts more goo than all of the Ghostbusters movies combined.

“I wasn’t worried about it,” says Depp matter-of-factly. “But when they dump that large an amount of an incredibly foreign substance on your face, you don’t know what to expect until it hits you. You don’t really rehearse that kind of thing, and so there is a part of you going, ‘God, I hope that this doesn’t shoot up my nostrils or down my throat. I don’t want to inhale the stuff and drown in slime on film.’ So that was little bit of a concern.”

Even though Pirates 2 was a more expensive production, Depp had a much less stressful time making it. While he was shooting the first film, the actor attracted the ire of Disney execs who were freaked-out by everything from his fey performance to his gold-capped teeth.

“It made it a little better for me that I wasn’t getting the panicked, worried phone calls saying, ‘What the hell are you doing? You’re ruining the movie!’ I didn’t get those this time around,” the actor says with a laugh. “That might have helped to add a little bit of spring to Jack’s step.”

You can’t really blame Disney for worrying about Depp’s performance. In the annals of unlikely superstars, no one appears to be a dodgier bet than Depp.

A one-time teen idol courtesy of TV’s 21 Jump Street, the actor spent his 20s and early 30s starring in oddball movies like Edward Scissorhands, Cry Baby, Ed Wood, Donnie Brasco and Dead Man that thrilled critics and diehard fans but left mainstream audiences cold. In 1998, he relocated to the South of France to raise a family with French actress/singer Vanessa Paradis.

Having kids, says Depp, changed his life in a big way.

“Being a dad made it easier for me to roll with the punches,” he explains. “It just put a lot of things into perspective for me, instant perspective. I think that for a number of years, I was frustrated by Hollywood, and didn’t understand any of it.

“But as soon as I knew we were going to have a baby, I found out what was important to me really quickly.”

A native of Kentucky who dreamed of being a rock god, Depp blames his bad experience on 21 Jump Street with souring him on conventional stardom.

“The show was great training because I was in front of a camera five days a week, nine months out of the year learning, learning, learning but it was also something where they were pushing me in a direction that I didn’t want to go,” says Depp.

“I really hated the idea of being a product on someone else’s terms.”

When 21 Jump Street producers balked at releasing Depp from his contract, he set about disrupting the set. He created so much commotion, he eventually won his freedom.

“I’m savvy enough to understand that there is a business side to all of this,” notes Depp. “But I swore to myself back then that I would do the things that I wanted to do and if I failed, I failed and if it worked, it worked, but that I was going to stick with [my plan].”

Some fans were surprised when Depp popped up in Pirates of the Caribbean, a Jerry Bruckheimer-produced flick that was based on, of all things, a Disneyland ride.

“For me, doing Pirates of the Caribbean was totally consistent with everything that I’ve done since Cry Baby,” says the actor. “There was never a moment when I thought that I’d do the film because it would be a good career move or that I could make a slew of cash and skate for a little while. I haven’t changed any of my processes or beliefs. I’m still dedicated to the same thing.”

And what does Depp make of his image being used to sell numerous products, including a new Pirates of the Caribbean ride?

“Oh, it’s totally surreal,” he says. “It’s teetering on absurd but a kind of great absurd. I’m honored.”

Since starring in Pirates of the Caribbean, nearly everything Depp has touched seems to turn to gold. Subsequent films like Charlie and The Chocolate Factory ($206 million), Finding Neverland ($51 million) and The Corpse Bride ($53 million) have delighted movie-goers and critics alike.

Depp might have the Midas touch at the moment but he has, so far, resisted the temptation to play it safe. For his next film, the actor plans to reteam with frequent collaborator Tim Burton for an adaptation of Stephen Sondheim’s Sweeney Todd, the pitch-black musical about a barber who redefines the notion of a close shave.

The film will be a particularly risky proposal for Depp, who claims he doesn’t have much of a singing voice.

“I might be a horrible singer but that could work for the character,” he says brightly. “I think it’s so important to challenge yourself and be potentially teetering on the brink of absolute flopdom because otherwise you’re just sort of there, taking up space.”