[avar]

I use git-annex which satisfies almost all of those requirements. I don't back up whole machines (why backup the OS when I can reinstall faster), but it otherwise has all those things.

[Mister_Snuggles]

I wasn't clear when I said "multiple machines" - I'm definitely not backing up whole machines!

It would be a case of multiple machines each backing up their /etc, /home, /var, etc to one place.