Network backup services are going to become big business, as everyone--businesses and consumers alike, figure out it is cheaper and easier to pay someone to store all your stuff. And the stuff is growing like crazy, as we buy songs online, download videos, and put thousands of digital pictures on our hard drives.
For purchased content like music and videos, you really should not have to back that stuff up; instead, the sellers should provide dead simple ways to re-download content you have already paid for, and as we buy more and more stuff online, it will become a business necessity to offer that service.
I recently bought some digital images for a new brochure, and accidentally deleted them. The firm I bought them from sent me replacements, but it took several days and I got a scolding email from them about how I should be more careful. Why on earth would a company scold a paying customer? It's just bad business, and that kind of attitude will slowly go away.
But content we create ourselves--years of email, family pictures, home videos, and other kinds of nonreplaceable data--needs more secure storage, and it really needs to be off site. What a lot of people are doing now is buying a cheap external hard drive and making a copy of everything there. That is good only to a point--that won't protect you against floods, fire, or burglary. And businesses have similar problems, as nearly all business data--customer information, product data, brochures, presentations, etc.--are in digital format.
Some people are using "free" services like Google Gmail to back some stuff up, but these free services have low quality of service compared to paid services, and they are not that expensive any more. FileBanc is a company that offers both consumer and business backup services, and Data Ensure is another firm that markets to businesses.