The suit was filed in Los Angeles against the companies which operate Morpheus, Grokster and Kazaa, which have risen to prominence since Napster suspended its service.
Films such as Planet of the Apes and Legally Blonde are available through the services as well as new music from releases from Bob Dylan and 'N Sync.
Companies including Disney, Capitol Records and Paramount Pictures, say the sites, run by Grokster Ltd, MusicCity.com Inc., MusicCity Networks and Consumer Empowerment BV, are profiting from copyright violation.
"We cannot sit idly by while these services continue to operate illegally, especially at a time when new legitimate services are being launched," said Hilary Rosen, president of the Recording Industry Association of America.
The action is seen as the industries' way of attempting to clamp down on file-swapping sites which have sprung up since Napster stopped trading illegally.
Napster shut down its services in July after a similar lawsuit filed by the music industry. It has vowed to be up-and-running with a legal service by the end of the year.
The suit states: "Defendants have created a 21st Century piratical bazaar where the unlawful exchange of protected materials takes place across the vast expanses of the internet."
'Self-sustaining'
The action faces a stumbling block because, unlike Napster, the three sites do not require a central company to create the downloadable files because they are swapped between users.
Music City chief executive Steve Griffin called the network "self-sustaining".
The provider of the software for all three services is an Amsterdam-based company known both as FastTrack, or Consumer Empowerment, which operates the Kazaa portal.
Grokster Ltd is registered on the tiny Caribbean island of Nevis, while Morpheus is based in Tennessee.
The big record companies are backing their own internet download services in the coming months but progress so far has been slow.
MusicNet is the joint venture between BMG, EMI and Warner while Pressplay is backed by Sony and Universal.
"After the injunction was issued against Napster, there was this great opportunity to say to consumers 'now the party's over and here's another service', but that's what they didn't do,"said Eric Scheirer, analyst with Forrester Research.
"It's not all surprising these other services have grown in popularity."