Operating under the sign of a Jolly Roger, The Pirate Bay website hopes to evoke a buccaneer spirit: swashbuckling swordsmen, or perhaps the pirate radio stations of the 1960s. But as the internet's number one destination for illegal downloads, it has raised the ­hackles of the entertainment industry and elevated its founders to the top of Hollywood's most wanted list.

With more than two million visitors every day, The Pirate Bay has become one of the sharpest thorns in the side of the media business. Its controversial success has caused havoc in the music, TV and film industries.

Current top downloads include The Bourne Ultimatum, Die Hard 4.0 and Knocked Up — all showing in British cinemas, but available to watch on a computer screen for those willing to take the risk.

The three-year campaign to bring down the website is almost an epic of Hollywood proportions, sprinkled with high-flying lawyers and accusations of political extremism. And yet, so far, the chase has failed to bring the pirates down.

Despite their high profile, however, the men behind The Pirate Bay are not part of an organised crime syndicate. Instead, they are an unlikely trio of Swedish computer geeks who began their war with the media from a small room in Stockholm.

The group, who spoke exclusively to the Guardian, live like students in the suburbs of Sweden's major cities. They wake late and work into the night. The closest thing they have to an official headquarters is a desk on the suburban outskirts of Malmo — and that is simply because it has a working fax machine.

But as the most hated men in Hollywood, they said they have become used to the attention. "We get legal threats every day, or we used to," said Peter Sunde, 28, one of the site's main workers. "But we don't have a problem with them — we're just a search engine."

Fredrik Neij, a 29-year-old IT consultant, has a more prosaic view: "It's nice to be noticed," he smiled.

Chief among those angered by The Pirate Bay's popularity is the Motion Picture Association of America (MPAA), which represents the US film studios. It is waging war against the site, which it claims is costing billions in lost sales.

John Malcolm, executive vice-president of the MPAA, has railed against the trio, accusing them of cashing in on illegal activity. "The bottom line is that the operators of The Pirate Bay, and others like them, are criminals who profit handsomely by facilitating the distribution of millions of copyrighted creative works," he said.

Mr Sunde insists the site does not profit its founders, and money raised from advertising is used to cover expenses. Instead, he says, the team make their money from a variety of side projects and day jobs.

Filesharing and illegal downloading has been a big issue for media companies since the late 1990s. But while pioneering services such as Napster and Kazaa were closed down by the courts, the campaign against The Pirate Bay has failed to make a breakthrough.

The crux of the defence is that The Pirate Bay operates like any internet search engine: it points to downloads, rather than hosting any illegal content itself. Under Swedish law this has so far made it immune to prosecution.

"I don't like the word untouchable, but we feel pretty safe," said Mr Sunde. He thinks that European enmity towards the Bush administration has bolstered support. "The US government is losing popularity every day in Europe, and people don't want to see us give in to them."

Their apparent invulnerability to prosecution has made them heroes of the internet piracy movement, but not everybody feels the same way.

"I certainly don't see them as romantic pirates: it's out and out theft," says John Kennedy, chief executive of the international music industry body IFPI. "It's pure, ruthless greed — or total naivety."

But the group's supporters around the world say they are vexed with what they see as the "corruption" of the media industry.

"This is already happening — you cannot stop it," says Magnus Eriksson of Piratbyran, the Swedish thinktank which helped start the website in 2003. "But the thing is that the people who download the most are also the ones who spend the most on buying media. Media companies already know that they have to change."

The pirates suspect the cam­paign against them is gathering pace. Last year police raided the site and held Gottfried Svartholm, the third member of the group, for questioning. No charges resulted, but the site was offline for two days.

Lately critics have focused on potential political links, including one German failed attempt to link the organisation with far-right extremists.

More recently Swedish police said they were considering blocking the website because of a tip-off that some pages linked to images of child abuse. This, says Mr Sunde, was just an attempt to smear The Pirate Bay's reputation. "There were three files in question, but it turned out that none of them contained child porn," he said.

The group is adamant it is just a search engine, but Mr Kennedy rejects any analogy with traditional internet businesses. "When I sit down with Google they are prepared to talk about copyright issues," he says. "If I thought The Pirate Bay guys were doing something really new and clever, then we'd look at it — but there's no evidence of that."

Mr Sunde remains unmoved. He says piracy is a way of life on the internet. "I started off copying disks on my computer when I was eight or nine," he said. "You should never tell people where they can't go or what they can't do."

· This article was amended on Monday September 17 2007. We said that The Pirate Bay website keeps an index of torrent files, pointing people in the direction of downloads "whether they are copyrighted or not". We should have said whether or not there are restrictions on their use.