So far, I love Google docs, with some limits. Like most faculty, I do a lot of work at home in the evenings and on weekends, so I end up schlepping computer files back and forth on a pen drive, or sending them through e-mail. The schlepping isn't a hassle, but inevitably there's something I forgot, and going back to campus to get it is a hassle. So, to the extent that Google docs allows you to work on a file anywhere and anytime you have internet access, it's a lovely thing.
There are a few downsides. For example, Google docs doesn't have a lot of fonts, and I'm something of a font snob, so that's a minor annoyance. As you might expect, Google's spell-checker isn't as good as Word's, and they don't have a thesaurus. So far, I haven't tried anything fancy, such as integrating pictures, and you can't do really fancy things, like mail merge, but the program works well as a basic word processor. If you need the fancy stuff, you can always download your work as a Word file and edit it there. The little problems are greatly outweighed by the advantage of working on your document at home, at work, or even while proctoring an exam, and never having to worry that you're working on an older version. It's all magically backed up in space, too!
Google docs lets you access your paper from anywhere, but you can't necessarily access all the PDFs of relevant literature, your data (depending on format), etc., etc. So, if there is a lot of material that you need at your fingertips in order to write, and you need to be at your office computer, anyway, then Google docs doesn't have many advantages over Word in that circumstance. Still, if you write on your office computer in Google docs, when the time comes to edit the paper, you can do so from home (or, in my fantasy world, from a warm beach, sipping little drinks with umbrellas).
I need a vacation. To a beach. With free wi-fi.