Although jail time and fines are a possibility, most attackers functioned behind proxies and botnets. Since drones were doing most of the work, the FBI may have difficulty pinning the attacks on the right people.
Anonymous took down the RIAA and MPAA websites in response to actions taken by antipiracy organizations. The group also targeted others over their antipiracy efforts, including Hustler magazine, Gene Simmons, the UK's BPI, and Aiplex, an Indian company that does antipiracy work for Bollywood studios. Other similar groups in France, Australia, Spain, and elsewhere were also targeted.
Anonymous says it wants to keep all information on the Internet free and available to everyone. In other words, to them, copyright is a form censorship.