Hackers have targeted the US government and copyright organisations following the shutdown of the Megaupload file-sharing website.
The Department of Justice (DoJ), FBI and the Motion Picture Association of America (MPAA) among others have been bombarded with internet traffic.
Web links have been been distributed which, when clicked, make the user's computer part of the attack.
A statement attributed to Anonymous claimed responsibility.
The DoJ announced on Thursday that it had taken action to force Megaupload and related domain names offline, and had charged the firm's co-founders and others with violating piracy laws.
Four of the employees have been arrested in Auckland, New Zealand, at the request of the US authorities.
Police also seized cash, valuable cars and a short-barrelled shotgun from the residence of the website's German founder, Kim Dotcom, formerly known as Kim Schmitz.
They appeared in court on Friday. One of their lawyers initially objected to media requests for photographs, but the accused said that they did not mind "because we have nothing to hide".
Their Hong Kong-based site had around 150 million users and 50 million daily hits. It had received celebrity endorsements from the model Kim Kardashian and singers Alicia Keys and Kanye West among others, making it one of the net's most high-profile file sharing sites.
The business had said it had been diligent in responding to complaints about pirated material.
News of the arrests came the day after thousands of websites had taken part in a "blackout" to protest against proposed anti-piracy laws; however, the DoJ suggested the two matters were not related.
A statement from the department noted thata grand jury indictmentagainst the Megaupload employees was issued on 5 January.
Hours later a statement linked to the @AnonymousWiki twitter account announced: "We Anonymous are launching our largest attack ever on government and music industry sites. Lulz. The FBI didn't think they would get away with this did they? They should have expected us."
It said that 10 sites had been taken offline in response to the Megaupload shutdown including the FBI, Universal Music, RIAA (Recording Industry Association of America) and Hadopi - the French government agency responsible for "protecting creative works on the internet".
On Friday,Universal's webpagesaid: "This site is under maintenance. Please expect it to be back shortly."
Hadopi was also offline, reporting "technical problems". However, the other sites on the Anonymous list all loaded.
Security firm Sophos's blog said that the attacks were carried out by spreading links via Twitter and other parts of the internet which carried outdistributed denial-of-service (DDoS) attacks.
It noted that such attacks were illegal, meaning that users taking part in the action were breaking the law.
A tweet from one of the accounts associated with Anonymous suggested that efforts were also being madeto resurrect Megaupload.
The attached link intermittently directed users to a site that resembled the shut down service. The address used a .bz domain name signalling it was registered in Belize.
However, one blogger warned that the site might be a scam designed to steal information from visitors to the page.
"Whenever file-sharing services go down, scammers and opportunists work quickly to ride on the wave of publicity generated by the targeted site's demise," said Andy Maxwell, co-editor of Torrentfreak.com.
"Megaupload is not yet 'back' and any site claiming to be them or says they're acting on their behalf should not be trusted."
Analysts say that there is a risk that the Anonymous campaign could become confused with the broader campaign against the House of Representatives' Stop Online Piracy Act (Sopa) and the Senate's Protect Intellectual Property Act (Pipa).
"The action against the US bills was based on websites voluntarily censoring themselves in order to protest the restriction and damage to the internet that these laws would cause," Dr Joss Wright, a fellow at the Oxford Internet Institute, told the BBC.
"In one sense the actions of Anonymous are themselves, anonymously and unaccountably, censoring websites in response to positions with which they disagree.
"The goals of many Anonymous activists are a free and open internet, but the regular and blanket denial-of-service campaigns could easily be counter-productive if pro-Sopa and pro-Pipa advocates can portray these actions as representative of those who are against this legislation."
Elsewhere, the inventor of the web, Sir Tim Berners-Lee, added his support to the campaign against Sopa.
He told the Inquirer theinternet needed to be protectedas an open space, adding that: "Folks in the UK should not be complacent. There are plenty of laws they should look out for already on the books that also have issues."
His comment may be a reference to the UK's Digital Economy Act, passed in 2010 but not fully implemented, and the Anti-Counterfeiting Trade Agreement (ACTA) which has the backing of the EU's Council of Ministers but has yet to be ratified by the European Parliament.
Candidates for the Republican Party's presidential nomination also weighed in on the matter at a debate on Thursday night.
Newt Gingrich said: "The bill in its current form is written really badly and leads to a range of censorship that is totally unacceptable."
Mitt Romney added: "A very broad law which gives the government the power to start stepping in to the internet and saying who can pass what to whom - I think that's a mistake."
Ron Paul, who has long opposed the law, said he was pleased to see other Republicans support his stance.
"This bill is not going to pass, but watch out for the next one," he added.
Rick Santorum said he did not support the law in its current form, but said: "I'm for freedom, but I'm not for people abusing the law and that's what's happening right now."
US Senate Democratic leader Harry Reid later announced he had postponed a vote on Pipa scheduled for next week.
Astatement released by his officesaid: "There is no reason that the legitimate issues raised by many about this bill cannot be resolved... I am optimistic that we can reach a compromise in the coming weeks."
However, Senator Reid did not provide a new date for the vote.
Europe's Digital Agenda CommissionerNeelie Kroes also tweetedon the subject: "Glad tide is turning on #SOPA: don't need bad legislation when should be safeguarding benefits of open net... Speeding is illegal too: but you don't put speed bumps on the motorway."
The MPAA defends the legislation saying that the bills will "encourage innovation while preserving millions of jobs that depend on intellectual property protection".