Take insurance!
Seriously, I think you will have other things to worry about if you loose your home.
However, there is some sense in your thinking. You have probably noticed virtual Internet "hard drive" sites that offer storage space. It's also possible to rent office software, use it and save documents over the Internet etc. However, in this case there would be outstanding practical, legal and even quality problems.
At first, somebody would have to build that very complicated system and keep it running. How much would you pay for it?
I would not like to replace my library with other people's various quality media files. Also, consider about the work you would have to do in gathering them back from all around the world. Even your personal work would probably be more expensive than a few large external USB2/Firewire HDs.
I have my work history starting from the year 1989 in my computers. Also, my personal photo library, mail archives, bookkeeping, tax calculations, Internet links, etc, etc, and of course my media library.
I don't like to lose any of them in case of fire, natural catastrophe of robbery.
So I keep one duplicate of my backups in a safe place outside of my home. I exchange that with the other updated one about weekly or so. It is not likely that I loose all three copies of my archives at the same time.
If the unbelievable happens and my home burns down (but I survive alive) I will still have a quite recent backup of my archives to start with after I have got a new home and computers.
Besides, I don't think it would be legal. You have legal rights to the peace you bought and Swedish laws allow you to make copies for personal use, but you have not bought a universal license for the intellectual work in case you lose the original product. You should calculate the risks and perhaps extend your insurance coverage if you like to play safe.