1. Compatibility with non-Windows platforms.
2. Faster loading than downloading assemblies.
3. Simpler security model at the client and server level.
4. Browsers work on a plethora of older machines.
5. Web canvas is more flexible for document operations.
6. More "hackable" (in a good way) interface: tabs, bookmarks, URLs, plug-ins.
7. Much easier to pass by corporate IT groups.
8. It already works, today.
9. Not every developer designs apps by dragging and dropping. Some of us use dynamic content generation, which is easier on the web.
10. Instance, seamless updates to all clients at once.
11. Why does your blog have a web interface? Planning on going to RSS-only at some point simply because RSS readers are "richer"?

If Windows-only, rich, winforms-capable, secured code was the way to replace web interfaces, we'd all be using ActiveX right now with enough of a thin film of HTML behind it to instantiate the object.

For scenarios where supporting a wide variety of clients is important, using a browser-based application does make more sense. Within the boundaries of an organization this usually isn't that important.

Smart clients provide a combination of the advantages of both web and windows-apps: there is more opportunity to optimize the use of the application with regards to usability and caching. Especially in scenarios where people use the application to perform their primary task, like data-entry, the gains that can be achieved by not having to contact the server or run tasks in the background, make a great deal of difference to the user. A large part of this functionality can be achieved thru the use of client-side javascript, but this requires a lot more effort. Especially when having to support multiple browsers.

The deployment has taken advantage of the lessons that were learned from webbased applications: being able to deploy new versions without having to touch the client-systems and using HTTP for communication. Wahoo (http://www.sellsbrothers.com/wahoo/) is a compelling example of the ease of deploying such an application. This is to become even easier with ClickOnce.
The main requirement is that the client has the CLR installed; with Windows 2003 and Windows Update this is becoming more and more common.

The difference between building a Windows-application and building a web-application still exists but has become a whole lot smaller with WinForms. Generating dynamic content and outputting this to a Windows-form, is very similar to doing this in ASP.NET.

Document operations like flowing text within a frame have limited support at this time; but this will be improved with both Whidbey and Longhorn.