There is an interesting article on Slate about an experimental "Web operating system" that a small team at MIT created. YouOS is an online platform with a window-based, graphical user interface. The service has handy applications on it, such as an RSS reader, an e-mail client, and a text editor. The team has opened up the platform so that other people can write applications for it, and many have--there are nearly 200 applications you can install on your own YouOS account.
One of the default applications on YouOS is a Web browser, which is ironic, since the browser runs under YouOS, which in turn is displayed in your computer's browser, which of course runs on your computer's operating system. It's the software version of Russian nesting dolls.
But I don't want to diminish what the team has created nor what they're working on: there's an integrated file system, built-in presence detection, and an architecture to spread computing load across the YouOS servers. Also, YouOS tracks a user's state across user sessions, which means that after you log off, you can log on from anywhere and your YouOS desktop and applications will be in the same state you left them. And it's supposed to be easy to develop for, to which the 200 applications attest.
I believe the next big Web 2.0 boom is not going to be a million more clever but small apps, but rather the release and ongoing improvement of big suites, such as Glide Effortless, Goowy, Veetro, NetSuite, Zoho, and perhaps an integrated suite from Google (as opposed to Google's current mishmash of online applications). I'm not convinced that we really need a general-purpose online operating system just yet, although the tools and concepts in YouOS might make a very useful platform for one of the new suites.