I'm calling it - time of death: June 2007. Its been a long time coming, but it seems clear that the Blackberry, the iPhone, Outlook, Picasa, and iTunes all herald the end of document-centric computing.
The iPhone really didn't create this trend, but I'll say that its certainly a very visible final nail, just as the Macintosh Finder was the "visible" start back in 1984. Today, you don't keep piles of stuff on your "desktop" and activate applications (or applets) against relevant document parts: the vast majority your content is organized against your applications, not the other way around - the iPhone is a computer that doesn't even have a desktop, in any traditional sense.
There was a brief resurgence of the idea that the document was the gateway to your applications in the early 90's with OpenDoc and OLE (Object Linking and Embedding).
We're at the starting tip of an orgasmic diarrhea of content creation in the form of e-mail, blog posts, music, photos and videos. And every single one of those is organized against single media form computing - barely a compound document in sight... you go to custom applications to create, edit, organize, and consume all the vast amount of gigabytes and terabytes of data we all share.
Vista Search and Spotlight in OS X only demonstrate even further how increasingly irrelevant the Finder and Windows Explorer are for everyday users.
In a slightly related tangent: What's most shocking to me today is how right Unix got it in the 1970's. URL's and hierarchical file paths seemed like dinosaur concepts in the early 90's before roaring back.
Either that, or we just haven't had the imagination to organize our way out of a paper bag since 1977... there's a parallel here.
Another way of saying "cool idea - wrong problem".