I use Mozy for backup at home on one of our laptops. It works pretty well. After Googling a bit it appears these backup / file sharing sites are popping up all over the place. Microsoft has SkyDrive and there is an apparently nefarious file sharing site called Ziddu, which I would stay away from because their site downloads trojans on your computer.
Microsoft’s SkyDrive looks like an excellent service. Read more here.