I have used Mozy for over a year without problems. However, I have never had to restore data and I share the previously mentioned concerns about my data being stored somewhere else.
I signed up with carbonite prior to Mozy, but could never get it to work. I tried contacting carbonite multiple times but just kept getting auto-generated e-mails. There was no telephone number to call for support. Eventually, I had to have my credit card company cancel the carbonite charge, which carbonite challenged, etc.
I even tried ordering something else on-line several months later from an unrelated company and they refused my credit card because the new company used the same credit card clearing firm as carbonite.
It was all a big mess and, needless to say, I was very dissatisfied with carbonite.