[zdw]

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.