I do think we are seeing the downfall of the operating system as we know it.
Its replacement? The internet, of course, with Google Docs being the obvious example of the kinds of applications which begin to make more sense online. Suddenly, any computer with a web browser offers the same access to and experience with my data, regardless of operating system. And it falls neatly in line with the fact that over the next ten years I will go through many iterations of hardware, and multiple operating systems, but my gmail account will most likely remain a constant. Generally, I want as much of my data (at least non-sensitive data) as possible tied to the most durable thing.
Once we reach the point where we can stream full-resolution video, nearly any application could theoretically be handled over the net. I wish I could find the article I was reading about taking video games in that direction. Video games, because of their high demands on processing, memory, graphics, and interaction, are easily the most rigorous standard for this model of computing. And they have a lot to gain from it. Taking user-purchased game consoles or pc hardware upgrades out of the equation would revolutionize that industry. The entry price would be much much lower, theoretically attracting a much larger audience. (With ad-based revenue, there may simply be no entry price.) And the experience could be much better, with hardware maintained and upgraded by the game publisher far outstripping the capabilities of mass-produced machines. Again, all you would need to access it is some sort of web browser. Most likely, this would come in the form of a box by your tv with controllers attached to it. The main problem here is that pesky speed of light, which absolutely limits the kind of response time you can get between your input and the result on the screen, based on distance to the server. But for games that do not require twitch reactions (alas, my favorite kind), it is in many ways an ideal platform.
So in this new world the operating system hopefully changes significantly, because it's got a lot less work to do. It's definitely well on its way. The purest example of this idea to date is gOS, which integrates Google's web applications into a stripped-down Linux build. A version of it is included with the $400 Cloudbook being sold at Walmart. It's got a long way to go, mainly because web-based applications have a long way to go. But I love the approach, which is to start with the bare minimum, and add things only as you need them.
It will be important for all of these web applications to automatically back up my data to my own hard drive or server, so I always have my own copy. In fact, I can think of a lot of great things about having one storage device in my house with which all of my devices interact via the internet or a local network. My camera, for instance, should be sending my pictures back to my computer (or to my online image editor, which then backs them up to my computer) as soon as it can find an internet connection, so I never run out of space on the card.