Crashplan does exactly as you mention, and handles jumping through NAT, encryption (with your own keys if you want), etc:
http://crashplan.com/
Cross platform (Mac/Win/Linux/Solaris). Some extra features unlock if you buy the + version.
If you want a totally free solution that would take a little more work to implement, look at Duplicity:
http://duplicity.nongnu.org/
rsync based, uses SSH/GnuPG for security.
Run one of these on whatever hardware you have available.