I recently skimmed by it on a Web application article and immediately recognized the name. But not because of the reviews or its service.
I remembered it from the commercials.
Mozy was advertising on Hulu for some time. I don't know if the ads are still going on Hulu because I haven't seen one in a while, but that is where I first saw it. The commercials usually featured someone using their computer in an average, everyday way and then something completely bizarre happens, like a stove falls out of the sky and directly on your laptop. Take home message: you never know what can happen to your computer.
But my favorite commercial was this guy who was clearly in a rush and accidently puts his laptop into the microwave instead of his frozen dinner. Yeah, I really felt for the guy too.
Here's the ad on YouTube:
I don't know if this was really the intent but this particular commercial really appealed to me, not because they were selling a useful or novel service, but simply because they essentially saying, "We understand that you are human and everyone has "OH %$&#!" moments in their lives."