You could implement SharePoint - Foundation is the free edition for Server 2008 x64, Windows SharePoint Services 3.0 would work on Server 2003. You could also buy SP Server; you asked for possibilities but don't mention your budget.
You can require check-in/check-out and implement version tracking on given documents or sites.
Edit - it looks like you're not really searching for the right terms. A versioning file system can do what you're asking for. VSS shadow copies are on the list, but they're not automatic, as discussed. Netware used to do this automatically, and so did VMS, but those aren't Windows Server. You could set up Subversion and WebDAV, but if you're going to do that, you might as well setup SharePoint Services and stay within the MS & Windows realm entirely.
There are plenty of free and commercial version-control systems (not fileystems), but those tend to be complex and aimed at software developers. If checkin/checkout is too advanced for your users, you probably don't want any of those and just want it baked into the fileystem, or as close as you can get.