I've been doing cloud backups for quite a while as I've been writing the below document for Computer Hope. I've had success with all of the online backups I've used, so far I've mainly just been focusing on paid subscriptions since they seem to offer all of the options I think most people would need including software that makes the process automatic, just like Calum mentioned earlier. Dropbox is also a great cloud storage, and I use them a lot also, but they don't really have any software that makes the process automatic and thoughtless. Although you can setup scripts and there other third-party tools to make it easier to backup.
http://www.computerhope.com/issues/chbackup.htmOne of the big concerns obviously with cloud storage/backup is security. You're posting information into the cloud where technically anyone could access the data. From what I've read though all of the paid services have great security, but that doesn't mean it's impossible for them to get hacked, just very unlikely.
Also, from what I last heard information that is in the cloud is not considered personal by most governments so a government could make a request to access your information and get access to the information much easier than they could if they had to get a warrant to seize your computer.
Finally, in the case of Megaupload, all of their servers were seized by the government and all information was lost. So, there is of course the chance that a service could be stopped and all information stored on their servers lost. Of course if you were just using it for a backup you should technically have all the information still, but if your computer died at the same time, and it was your only backup then you would be out of luck.