From bitter experience I've learned how important it is to back your files up regularly. But what if your backup computer fails?
There is actually a number of websites available out there.
I suggest you try out Data Deposit Box — you get a 14-day free trial after which it charges pretty much next to nothing should you choose to continue using it.
You download the Data Deposit Box software onto your computer, install it, and let it do its thing. Initially it's going to backup all the files you specify, after which it will automatically backup your files as you go along.
It runs in the background and automatically backs up any files you changed. It's also encrypted and you are the only one that will have a key to access your files.
Other online backup services that you can also give a go are MyDataBus, OmniDrive and MediaMax.
Give them a go and decide on the one that works the best for you!