Comparing WPF to Other Options
If you are solely a .NET developer, you really have only two other options to consider: Windows Forms and ASP.NET. We've already compared WPF to Windows Forms throughout the course of this hour. The only real advantages that Windows Forms has are its mature library of controls and significant third-party support. WPF is still the new kid on the block, and the mass of supporting tools and materials has not had time to build up yet.
Comparing WPF to ASP.NET is a little more involved. The question here really centers on deployment and distribution. WPF is currently limited to the Windows platform, and there's obviously no such limitation with a web application. WPF requires the .NET Framework 3.0 or later, as well as a means of deploying the application. If your application is centralized, requiring one or more server components, you are likely to reduce the complexity significantly by choosing to develop a web application.
Outside of the .NET world, some of the same features are available with Adobe Flash, primarily when it comes to media and animation. Historically, Flash has really only been useful in a Web context. However, the Adobe AIR platform utilizes Flash for developing cross-platform, desktop applications. Nevertheless, Flash still has some notable drawbacks. The development environment is not as robust as .NET although, admittedly, Flash does tend to be more designer friendly. Control libraries for Flash are much more limited and cumbersome to use. It is possible that AIR will provide some healthy competition for WPF.