Gnutella is a decentralized peer-to-peer network architecture primarily used for searching and downloading files. It was initially developed as a small Windows program by Justin Frankel of Nullsoft, an AOL-owned company most famous for its Winamp media player. AOL pulled the plug in early 2000 and ordered Nullsoft to cease all development but realized that they didn't have control over Gnutella's usage. The source code of Gnutella was intended to be eventually released under the GPL (thus the "GNU" in its name) but those plans were crushed by AOL's early intervention (which may have well been the result of an early Slashdot* Effect that directed attention at the project).
Gnutella is a popular alternative to the OpenNap network. The protocol is open source, and so are most of the clients. Gnutella is a generally decentralized network and was originally created/supported in response to perceived and real threats towards centralized bodies like Napster. The thought behind decentralization is that no one broken link can bring about the downfall of all members.