I have some expertise in this area[1] so I would like to provide some additional information for future readers of this thread - specifically on rsync snapshots, rsnapshot, duplicity, attic and borg.
The simplest thing to do is to rsync from one system to another. Very simple, but the problem is it's just a "dumb mirror" - there is no history, no versions in the past (snapshots in time) and every day you do your rsync, you risk clobbering old data that you won't realize you need until tomorrow.
So the next thing to do is graduate to "rsync snapshots" - sometimes known as "hard link snapshots". The originator of this method was Mike Rubel[2]. What you are doing here is making a
hard links only copy of yesterdays backup (which means it takes up no space, since it's just hard links) and then doing your "dumb rsync". Any files that changed will break the hard links and your snapshot from yesterday will take up as much space on disk as (the total size of all files that changed since yesterday). It's very simple, very elegant, and requires no software support or requirements on the remote end - as long as you can ssh to the server and run rsync/cp/rm it will work.
Next step is to stop writing the (very simple) rsync snapshot scripts and let rsnapshot do it for you. We've never recommended this, since the rsync snapshot script is so simple, and rsnapshot requires that you put it on the server side ... so it's not as lightweight or universal. As far as we know, it's terrific, bulletproof software.
(Here is a good spot to point out that Apples "Time Machine" backup tool is nothing but rsync and hard link snapshots - that's all it is. Super simple, super basic - so you and a lot of people you know may have been using rsync snapshots for years without even knowing it)
There's one problem with these methods and that is the resulting, remote backups are not encrypted. Your provider, or host (rsync.net, for instance) can theoretically see your data. If this is a problem, you need something other than rsync.
The answer to this problem since 2006 or so has been duplicity.[3] duplicity is wonderful software, has a long history of stable, well organized development, and we have even contributed funds toward its development in the past. The problem with duplicity is that, due to some design constraints that I am not going to go into, every month or two or three you're going to have to re-upload your entire dataset again. The whole thing. That might not matter to you (small datasets) or it might be a deal killer (multi terabytes over WAN).
So now we come to attic and borg - borg being a more recently and more actively developed fork of attic. attic/borg give you all the network efficiency of rsync (changes only updates over network) and all of the remote-side encryption and variable retention of duplicity (and rdiff-backup) but without any of the gotchas of duplicity. Some folks refer to attic/borg as "the holy grail of network backups"[4].
We[5] are the only remote backup / cloud storage provider with support for attic and borg[6]. However, we are
also the only provider running a ZFS based platform[7] on the remote end. This means two things: If you
don't require remotely encrypted backups, you can just do a "dumb rsync" to us, completely neglecting any kind of retention, and we will do ZFS snapshots of your data on the server side. It's like having Apples time machine in the cloud. OR, IF YOU DO require remotely encrypted backups, you can just point attic or borg at us and solve the problem that way. Either way, you're getting the one thing nobody else will give you - a plain old unix filesystem, in the cloud, that you can do whatever you want with.
[1] I am the owner and founder of rsync.net.
[2]
http://www.mikerubel.org/computers/rsync_snapshots/
[3]
http://duplicity.nongnu.org/
[4]
https://www.stavros.io/posts/holy-grail-backups/
[5]
http://www.rsync.net
[6]
http://rsync.net/products/attic.html
[7]
http://rsync.net/products/zfs.html