In a word: hogwash.  In fact, I think the time is long overdue to file this .com-era fallacy away next to "Super Bowl ads are a great idea for startups", "drawing an audience is more important than making a profit," and "people will totally buy dog food online."
 
It seems that every time a cool, new web app comes out, the chorus of "boy, if they can do that, pretty soon we'll just be doing everything in a web browser" starts up again.  It's a cute thought, but it really is so Flat Earth Society.  Despite overwhelming contrary evidence, some folks insist on clinging to the notion that one day we'll do everything in the browser.  It's a classic slippery slope argument: Because Web applications are increasingly cool and functional and constantly becoming ever more rich and more capable, we must logically be able to conclude that they'll some day get to the point where the web replaces traditional apps, right? Um, no.
 
In fact, the preponderance of evidence suggests just the opposite.  Hardware and software innovations enable more and more intelligence to be pushed to network endpoints.  Web PCs have thus far been a commercial failure.  Our reliance on the Internet grows while our use of the web as Chief Internet Vehicle shrinks.
 
Intelligence at the Endpoints
We're progressing in a direction where every device is increasingly powerful, capable, and connected.  People and businesses tend to prefer devices with more processing power, more storage, more connectivity options, and more desirable form factors.  This is a trend that shows no signs of reversing.  Rather than a centralized web client/server model, we are moving inexorably toward a distributed computing world, where all network endpoints are all masters of their domain.  Every device on the network will be intelligent enough to do serious computing for itself and have enough storage to work locally with substantial amounts of data.
 
It requires very little rocket science to see that wired and wireless data pipes will soon be ubiquitous, wide, and fast.  But while connectivity may be king, but it will never be practical nor desirable for 100% of devices will to remain connected 100% of the time.  As a result, people will continue to gravitate toward devices that can grab data from a variety of locations, work with it online and offline, and synchronize data back to repositories.  An environment that forces full time connectivity is a productivity dog leash.
 
The line of thinking that dictates "some day, all PCs will be web terminals with nifty displays controlled by brilliant servers in the cloud" ignores a fundamental reality: hardware is getting better, smaller, and cheaper at a ridiculous pace.  Dollar for dollar, devices continue to get better.  Given this reality, I have a lot of trouble seeing the argument that this trend we'll suddenly stop and we'll all decide that our hardware has gotten good enough, thanks, and we're ready to give over our computing experiences to a web browser.
 
Remember the NC?
Economics, some argue, is what will drive this shift to the web PC.  But this argument, too, is unsupported by reality.  The delta between in the cost to produce a "smart" device and a "dumb" device is very small.  In fact, it could be argued that, in many cases, smart devices are cheaper to produce than dumb ones, because of the economies of scale created by the IT industry being geared toward production of smart hardware and software.  And in the customers' eyes, some modest savings certainly isn't worth the dramatic reduction in utility and functionality.
 
As I was browsing the web, doing a little research on this topic, I came across this entertaining CNET article from 1996, touting Oracle's $500 Internet PC.  Known as the Oracle Network Computer, this device was arguably the poster child for the web workstation, "designed as a low-cost alternative to PCs for Net surfing, email, and word processing and other tasks that don't demand the processing power that a real PC offers."  For $500, you too could buy a virtually inextensible Network Computer with a closed OS and no hard disk or monitor.  Of course, the market failed to embrace this device.  After spinning off this offer to a separate company called Network Computer, Inc., a new, cheaper, Linux-based device was launched; $376 then got you a device with a Pentium CPU, small amount of RAM, 15" CRT, and CD drive.  A number of other companies entered the web PC fray as well, including Microsoft and partners, with the NetPC.  Few purchased these devices, and ultimately the product lines died and some of the companies behind them folded.  Somewhat amusingly, Network Computer's old domain of nc.com is now a tiny link page for North Carolina businesses.  By the way, I can go to Dell today and, for $549, buy a new entry-level PC that includes a 2.66 Ghz processor, 512M of RAM, 80 Gig hard disk, DVD/CD drive, 15" flat panel screen, color printer (!), Windows XP, and a variety of bundled software.  And, with history as a guide, it would seem prices will continue to drop for fully featured PCs.  With power so cheap, what incentive is there to choose otherwise?
 
Some would argue that the cost of ownership in certain circumstances is much cheaper for machines with limited functionality, and I agree with this.  I won't say that there is no need for a browser appliance ever; that would be silly.  Clearly there are some scenarios where a browser appliance is a great fit... a web kiosk, for example.  However, my point is that such devices are not destined to achieve broad market adoption among individuals and businesses.
 
Web Services and RSS
A legitimate case can be made that we are reducing our dependencies on the web even as we increase our dependencies on the Internet.  Web Services, for example, provide us access to the engines the power the web (and other things) from our own thick client applications.  Similarly, the success of RSS and thick client readers/aggregators, demonstrates the overwhelming demand for access to the web's content outside of web browser captivity.  There are of course many other examples of these types of technology, such as NNTP readers, web mail POP clients, web screen scrapers, etc.  Almost all of the tools in this category have enormous adoption rates, and each has a similar goal: to make available to all kinds of clients that functionality and content normally found on the web.  We may already be heading away from the web browser in many respects, not toward it.
 
So, please, spare me your tired the-browser-OS-is-coming proclamations.  It just ain't gonna happen.