I think it's brilliant... If you trust the internet. You can use "your" computer from anywhere in the world, and don't need to worry about broken computers, upgrading hardware, backing up data, or viruses, much the same way we no longer have to worry about prioritizing all of the tasks our computer will run for the next 36 hours. It's removing the part about computers that everybody hates to deal with and leaves just the interface and experience.
With google running it, it makes the most sense. They're the ones who have been moving the desktop to the web for years now, with their google docs, etc. We've also seen other things moving web-based as well, for example the image and audio editors somebody had posted a link to not long ago. Some very surprising things are also making it online. I played a full 3d game in the browser not too long ago. (Lego star wars. Check out starwars.lego.com).
But then, you lose a lot of control over your computer. There are many things you will not be able to do, that you can do now. However the bug question is: do you care? How many of the things you are losing can you live without, or can you replicate those things online. In most cases, I would go for it.
Then again, if you are paranoid and think the government is watching you, it may not be for you. But if they really wanted to watch you, I don't think they'd let trivialities like not being online stop them.