I suggest you look into sparkleshare. It provides many of the features of dropbox or ubuntu one (and could integrate with them) and may work on generic UNIX. if it doesn't you might consider using vanilla git, instead.
Barring that, setting up a cron job that ssh's to the server on a schedule and downloads the files would be a viable option.
the script run by the cron job could be as simple as
ssh user@remote_host "tar -cf - ~" | bzip2 -zc | cat > ~/dropbox/$(date | sed 's/\ /\-/ig')-rhost_backup.tar
or in laymans terms: "using ssh, on remote system call: 'create an archive of %HOME_DIR% and dump it into the console' zip that with bzip2, and put that in a timestamped file in my dropbox (assuming your dropbox is at ~/dropbox).
Obviously, this makes some asumptions about your client system, etc. There are probably ways you could do this on windows, Mac should be very similar. There are also options for tar that will allow you to only store new versions of the files, etc.