Well, you can make and analogy about cloud computing being the dumb terminal -> mainframe of the modern age but I still think that a purely online OS* is not so useful as well as hard to implement/design.
Cloud computing offers scalability and is efficient especially for web apps, which require more resources than normal websites (would you host your Wordpress blog or simple HTML website on such a service?) and tend to fluctuate in resource need. As it's been said before, this solution is not new but has gained more popularity in the 'recent' advent of Web 2.0 and webapps.
Another issue with storing data in the cloud is privacy: now I can unplug my PC and be sure that my data can not be accessed by anyone else except me (assuming that I can restrict physical access to the machine), when switching my data to online I can never be sure 100% that no one else has unauthorized access to it. But that's just the paranoid approach, I have lots of data in the cloud.
*by a purely online OS I mean no local storage and offline capabilities of any kind like those introduced by Google Gears, Adobe AIR, Microsoft Silverlight etc.