I run a windows server 2003 pc at home, server 2003 is a great little web server that can handle multiple roles, including file storage. Unfortunately it is not Upnp (universal Plug and Play) so will not stream media directly to media players like Xbox 360 consoles, and the Playstation 3.
The traditional (and recommended) solution to this is to stream the media through another more modern operating system that has upnp / dnla connections that reside in Windows Media player. This can restrict where you store files on a network, I for one do not want to store media on a desktop machine that I rebuild every 4-6 months.
Another solution to this is to use a software application that acts as a translation layer. There are a few around, but the one I've been testing out recently is the Twonky Media Suite. It installs as a software service, and sits quietly in the background and serves up any media requests that hit it. It also appears on the network as a Upnp device, so it will be found by media players, and consoles.
Simply install the trial version, in the setup manager point to your media directories, and then fire up your media player. It will find it and allow you to browse through the different media types, completely bypassing the need for windows media center connections, or operating systems that are a little too old to know about Upnp or dnla.