The term "open source server" just took on a whole new meaning.
OpenSearchServer is an open source application server allowing development of index-based applications like search engines.
Subsonic, an open source media server.
The Enhydra Server, an open source software application server developed by the Enhydra.org community.
Caudium is an open source web server.
PulseAudio is an open source sound server that supports advanced software mixing capabilities and network transparency.
I hope that their open source server, as soon as it's ready, gets adopted.
Subsonic is an open source, web-based media server.
CasparCG is a free and open source playout server and various clients.
Apache is an open source web server, the most popular in use.