AutoVer is a simple free backup tool which monitors the folders you specify, detects any new or modified files, and immediately backs them up to a local folder or FTP server.
The program can run as a straight backup, keep copies of every version of a file, or use your own custom versioning rate (save only one version every x hours, say).
Convenient archiving options can delete or zip up versions once they're older than a specified number of days.
A built-in file explorer makes it reasonably easy to find and restore files. Browse to the folder you need, click any file and you'll see a list of versions. These can be opened immediately with your usual applications, and there's also support for comparing file versions, although you'll need to set this up using an external application (it comes configured for WinMerge, but you must download and install this yourself).
If that's not enough, an option to run a custom program on every file change presents you with all kinds of additional possibilities. If you need to know an important application is running properly all the time, say, you could have AutoVer look for updates to a text log, and send an email alert (or maybe the entire file) if it changes.
AutoVer is a little basic in places, and has a few surprising omissions. There's no Search tool in the internal browser, for instance - you have to find and select files manually. But it's also easy to set up, very configurable, and on balance probably a good choice for a small-scale real-time versioning system.