Songbird has a pretty good replica of iTunes' media streaming capabilities, including the ability to stream from an iTunes hosted library.
iTunes serves up music via the DAAP protocol, so most of the mainstream DAAP clients listed here should do the trick. I know that Songbird and XBMC work well from personal experience, but many of the others should work as well.
If you'd prefer a more universal solution for streaming music to arbitrary computers (though this one isn't free), you could try RogueAmoeba's Airfoil. It is a stable and simple universal audio streamer that also supports direct streaming from iTunes, among other clients (or just your system's whole audio stream).
If you really dislike having iTunes at all, you could replace its media streaming functionality with Tangerine (mentioned in the Wiki article linked above), or another non-Apple DAAP server. Once configured, those products behave just like an iTunes music server on your network. Only, you know, without all the bloat and chrome.