Mozy, not Mozi.
Just don't entrust your valuable data to Mozzy. There's no telling what he and Neal Caffrey might do with it... /g
On a serious note, while there are some valid reasons to use these online storage services, e.g. convenience, people need to keep in mind that there are also caveats and vulnerabilities to consider. For example, the assumption that online access will always be available to them is dangerously naive.
In a time of emergency, natural disaster, terrorist attack or simply arbitrary government fiat, access to your data may frozen or impossible. In addition, if a company's servers are hacked your data is vulnerable, and likewise if you or your company somehow makes it onto some "alphabet agency's" enemies list. In the event of some sort of declared national "state of emergency" there's no guarantee of even having internet service "privileges".
Secondly, for most people, it's more secure and cost effective to buy your own external hard drive backups. You can buy two or three drives, or even a RAID NAS (Network Attached Storage) unit for much less than the subscription fees for online storage.
Finally, it's not just data that needs to be backed up. You really need bootable image backups of your whole hard drives, operating system, applications and settings, and they need to be accessible in case of complete system failure. Having those on external hard drives in your possession is far more logical and practical than trusting you'll be able to retrieve them online in the event of an emergency.
The bottom line for me is that there's nothing wrong with using these types of services for convenience if your security requirements permit, but it would be extremely dangerous to rely on them solely.