Peer-to-Peer networks are nowadays one of the common mechanism for distribution of pirated content. One of the first peer-to-peer networks was Napster. Some of the common ones nowadays are BitTorrent and LimeWare.
The RIAA was infamous for it's P2P lawsuits. The first lawsuits were filed in 2003. At first, they used DMCA subpoenas and based on them sued people directly. Later, threat letters that allowed defendants to settle without a lawsuit by paying were sent. On December 19, 2003, a federal appeals court ruled that RIAA's use of DMCA subpoenas were illegal. Next year, the RIAA began filing mass "John Doe" lawsuits instead. This was a great improvement over DMCA subpoenas that it allowed judicial oversight and an opportunity for a defense. Even after that, there were problems. One problem is that of the many people sues, some were poor people who could not afford to settle or defend. They even sued a dead grandmother, a 14 years old kid (which was dismissed due to failure to pay a guardian), a disabled person, and of course more. Another problem was how the IP addresses were gathered using MediaSentry. It was reported that MediaSentry lacked a private investigator license needed for this type of job, for one thing. Another that it sometimes used indirect detection which was inaccurate, with a researcher managing to be sent a DMCA notice for a printer!
Of course, that was far from the only P2P lawsuit. When P2P tech first appeared, they first tried to sue the technology itself. Napster shut down in July 2001 after it was sued. Also of course trackers and others were sued too, like the Pirate Bay.
The most recent mass P2P lawsuit is the one by the US Copyright Group, which used joinder to sue many defendents in one lawsuit. The EFF tried to declare this abuse of joinder illegal in an amicus brief, and while this failed to convince the court, this did led the court to order user-friendly notices for those targeted.