ZNC - znc is an IRC proxy. It runs as a daemon and connects to IRC server, then allows you to connect...
Shout - The self-hosted web IRC client
The Lounge - The Lounge is a web IRC client that you host on your own server.
UnrealIRCd - UnrealIRCd is an Open Source IRC Server, serving thousands of networks since 1999.
Quassel IRC - Quassel IRC is a modern, cross-platform, distributed IRC client based on the Qt4 framework.
irssi - Irssi is a terminal based IRC client for UNIX systems.