Why Back Up?
Because They Don't Care About You
Technology is business, and in business, money often takes priority over ethics. With the law perpetually lagging behind technology and business, there is often nothing between you and getting screwed over besides your own volition.
Corporations do not contemplate their own inevitable end. At least, they don't do it in public, unless they are in really bad shape. When times are good, those thoughts are pushed away, and end users are encouraged to do the same. When times are bad, they tend to go very bad, very quickly - if you're lucky, you'll have an announcement. Your data is never totally safe. Backing up your data is always necessary, even if it's stored elsewhere.
Disaster Will Strike
Entropy will rear its head, if you leave things up to chance. You will lose 4 years worth of email, including communications from the early days of your marriage, and the receipt to that flat panel monitor you bought online that now has tons of dead pixels. It doesn't take much for catastrophic data loss; one absent-minded mistake, or the ravages of time, can wipe out years of data.
There is real convenience to web services like Google Apps. It's tempting to get wrapped up in that convenience and never take a step outside of it. With a little work, convenience can be evenly matched with user control and agency.
Businesses can be extremely helpful, but they are also self-interested. As benevolent as Web services present themselves to be, your data is valuable to them - they aren't running this for your benefit. And it should be valuable to you, too.
But There Is Still Hope
Luckily, a few basic (and cheap) precautions can bring the long-term care of your data into your own hands, away from the short-term world of the Internet.
In information theory, entropy is often defined as "the loss of useful information."  In historical research, all information is useful. For the historical benefit of future generations it is essential to organize a concentrated effort against information entropy.
Despite our best efforts, some information will always be lost, but what is saved may help form the foundations of future cultures.