The hackers decided to attack the Paypal website after it suspended payments to the Wikileaks fundraising account.
The group has previously attacked the websites of Visa, Mastercard and the Swedish government. It has already attacked the websites of Visa, Mastercard and the Swedish government.
The hackers were also planning an attack on the website of Amazon, the online retailer, but opted not to after a split between its members.
One of the hackers said: "We attacked VISA and MasterCard's front end website, which is the page you see when you load visa.com or mastercard.com. We did not attack the payment mechanism for those two, but we did so with Paypal."
"It is definitely an information war. The core principle behind it is [that] information is free, governments keep information to themselves, Wikileaks releases them to the general public and the war occurs."
A spokesman for Paypal insisted that the site had not been disrupted: "As far as we are aware there hasn't been any further impact no the site and it remains fully functional."
Earlier the attackers brought down the official Swedish government website in revenge for accusations of rape in the country against WikiLeaks founder Julian Assange.
The official site, regeringen.se, was offline for several hours overnight and only a message saying the site could not be reached was visible.
The actions so far have been essentially attacks by volume, known as DDoS or distributed denial of service, in which the target site is hit with massively increased numbers of visitors with the intention of exceeding its capabilities and forcing it to crash.
In this case, hundreds of volunteers have downloaded something called a botnet, which aids the distribution of the command to attack the site. The volunteers wait until they are given a signal on an internet chatroom, before launching the massed attack.
The attacks are illegal in Britain and carry a maximum sentence of two years.
Internet security experts warned that Amazon could be next after the firm removed WikiLeaks contents from one of its services.
Carole Theriault, a senior security consultant at Sophos, a computer security firm, said: "If the big companies weren't locking down their information before, they're definitely doing it now.
"This is really unprecedented and Amazon could be next."
She added: "Hacking is illegal and it's not just the companies which are the victims of this, it's also the people who are trying to use their services to shop and the sellers of those items who can't sell them.
However she said it was unlikely, although not impossible, for people's credit card details to be unearthed by such attacks.
"Data held by financial services companies is extremely safe and it's in their interests to keep it that way."
The group of "hacktivists" calling themselves Anonymous posted a blog setting out its aims as campaiging for free speech.
The post read: "Hello World. We are Anonymous. What you do or do not know about us is irrelevant. We have decided to write to you, the media, and all citizens of the free world at large to inform you of the message, our intentions, potential targets, and our ongoing peaceful campaign for freedom.
"The message is simple: freedom of speech. Anonymous is peacefully campaigning for freedom of speech everywhere in all forms. Freedom of speech for: the internet, for journalism and journalists, and citizens of the world at large. Regardless of what you think or have to say; Anonymous is campaigning for you."