There are very good reasons why this combination hasn't been particularly popular. C++ with a few libs like MFC or WTL continues to rule on Windows being slowly replaced by .NET stack, Obj-C keeps rocking on OSX and C/C++ with Qt/GTK doing their job on Linux/BSD. Why is that? I suspect because of 3 reasons: very weak JVM penetration on the desktop, JVM is too heavy for most applications and because JDK-based UI feels foreign on every platform.
Developing a desktop application on JDK means that your users will have to deal with 100MB+ downloads followed by quirky installation process that rewards the with less then stellar UI experience at the end, especially the slow startup time.
Startup time is more important than most developers think: majority of desktop apps absolutely need it: imagine 5-second delay every time you wanted to launch Apple's "Quick View" to glance at a file, or imagine 5+ JVM-based apps load&initialize after reboot. Most desktop software I worked on was small-to-medium size and we just couldn't afford to add those 5+ seconds on JVM initialization. JVM I guess will work OK for projects like Ecilpse or a big Office suite or something like Photoshop. Microsoft understands this very well, this is why C#/.NET is so carefully optimized around loading time and comes with precompilation tools that essentially turn your C# code (including .NET itself) into native Win32 modules.
One project I want to do for myself is a usable Del.icio.us client for OSX. I can't see how I can use JVM-based tools for that... I want instant start-up by a hotkey when I need to search for links or add one. Moreover, I want users to be able to download and try it under 20 seconds.
The only JDKUI apps I'v ever used were development tools for Java itself plus numerous crap for the enterprise. And, of course, every once in a while I get "Java. Please wait..." splash screen on a new cellphone, followed by a prompt "Cancel/Go Back" keypress: that pretty much sums up my JVM-based UI experience. Which is sad: Clojure is going to be locked up on the server just like Java has been for years.