Apple's Time Machine is a great feature in their OS, and Linux has almost all of the required technology already built in to recreate it. This is a simple GUI to make it easy to use.
Installation is very simple provided you're running a modern distribution.
Installation Instructions (Linux)
There are no formal releases, just whatever is in subversion. From your install directory, run:
PS: I am not affiliated with Apple, nor have I even used Time Machine personally. Please don't sue me.