Some of the software options for getting this done include:
SHOUTcast is one of the original free Internet radio software solutions for streaming audio. You can start your own station fairly easily and the software is free to download.
Helix Server Basic
Free streaming media server software which can distribute live and on-demand video and other media. Realnetworks.com describes it as: "Simple 5-stream server. This free media server is a great solution if you are getting started with streaming media and want to experiment before rolling it out to a large audience." The Helix Server Basic is free to download.
Quicktime Streaming Server
Apple.com says: "Whether you are looking to add streaming media to your web site, deliver distance learning or provide rich content for your mobile subscribers, Mac OS X Server has all of the tools you need. QuickTime Streaming Server lets you deliver live or prerecorded content in real time over the Internet." You can find out more at apple.com.
Apple.com writes: "Combining the power of QuickTime with Apple's ease of use, QuickTime Broadcaster allows just about anyone to produce a live broadcast event." Download this software from apple.com
Peercast.org is a non-profit website that provides free peer-to-peer broadcasting software. "PeerCast is a simple, free way to listen to radio and watch video on the Internet. It uses P2P technology to let anyone become a broadcaster without the costs of traditional streaming," according to the peercast.org website.
Icecast is "free server software for streaming multimedia." Download a copy from icecast.org.
Andromeda is delivery-on-demand software. "Andromeda scans your MP3s and presents them as a fully-featured streaming Web site. That means you simply add, move, rename, and delete files and folders to update the contents of your Andromeda-powered site. It's as easy as drag, drop, stream," according to turnstyle.com where you can download an evaluation copy.