Various web cognoscenti have been ballyhooing the 'OS' concept in a web context: Google OS. This has more to do with the coolness factor of any new software development arena than with actual functionality provided by the respective software.
The Google suite offers the following:
GoogleDesktop (supposedly at the core of the 'OS', and a resource hog to boot!)
Audacity (audio editing)
Orkut (social networking)
Gdrive (internet data storage)
Other than Gdrive, none of the above belong to an OS.
Leaving coolness aside, there are genuinely innovative Web-based applications whose complexity is close enough to that of desktop-based applications. For example, computadora.de 's shell is not that different from Windows 95's shell as far as the basic functionality it offers. Flash is a kind of Win32 in this case.
On the middle layer, salesforce.com is a good example of application domain functionality provided by a Web-based layer. It should be entirely possible to offer a payroll processing service.
And yes, I have a computadora.de account. You can even upload mp3's there and play them using the integrated mp3 player – which I did, an Alejandro Fernandes song, in keeping with the Mexican origin of the software.