Frostwire: Limewire's open source cousin
Enter Frostwire. virtually indiscernible from Limewire, this program works just fine. It allows the user to download just about any kind of file from a massive community of Limewire and Gnutella users. Hypothetically it's possible to get copyrighted music as well, but you'd never even think about such a thing, we're sure.
Frostwire is available for Windows, OS X, and Linux. Ubuntu and Debian users can grab it from Synaptic, and everyone else can check out the download site.