Since 2003, the RIAA has sued thousands of college students, faculty, and parents across the U. S. for what it asserts is illegal file trading of mp3 tracks via P2P networks. They also send "pre-litigation" letters to users asserting illegal music downloads and demanding a settlement that, typically, is in the thousands.
In many cases, the RIAA has sued the wrong people. They sued an elderly woman who exclusively uses a Macintosh, and accused her of using a Windows-only application, Kazaa, to download many mp3 files of explicit rap music. Eventually, the RIAA withdrew its suit. Part of the difficulty in the RIAA's approach is that it attempts to force ISPs, particularly those at universities, to identify individual users by IP numbers. This is less than reasonable given that most ISPs and campuses use temporary IP leases. Any number of users use the same IP number, at different times. It's expensive, and sometimes impossible, to identify an individual user in the past. You can read a summary here of the RIAA's litigation efforts.