The incredible advantage that Desktop application have on web application is the connection with the local computer (other application, file system, computation, …). Unfortunately the mix between AIR and desktop properties are not as far as Java or C. The most wanted functionalities are to launch native application through AIR and integration with native libraries.
There are not a lot of work around: commandproxy, is aimed to bridge the communication between AIR and .NET.
Another project is Artemis but it was abandoned. Today the project rebirth under the name of Merapi.
Merapi use Java to connect AIR to the desktop. The project will be (unfortunately not yet) distributed as a freeware and then as an open source project on Google Code.
Here you can find information on Merapi and the here about the signification of Merapi.
I wish them a lot of success and I can’t wait to test it 🙂