Christophe Coenraets released the code Code from his MAX session in Barcelona about Offline Synchronization using AIR and Live Cycle Data Services.
Rich Tretola (Everythingflex) posted an update of his AIR Update Manager. With the Update Manager you can define the version and update URL of your AIR application and also all dialogs regarding the update can be set. Another nice example by him is the AIR Context Menu.
Eric Feminella blogged an AIR extension for Cairngorm. I have not tested it yet but it looks interesting. I have already developed AIR apps with Cairngorm and there is no big difference to Flex web applications.
The badge install for AIR is one of the coolest things looking at the using experience when installing an AIR Application and the runtime itself. Oliver Goldman from the AIR Team posted about an update which closes a security hole.
When you are new to AIR be sure to check the AIR Showcase and when you start learning AIR be sure to check the Adobe AIR Developer Center which is part of the new launched Adobe Developer Connection. For more on this check the latest Adobe newsletter which provides many interesting links for learning resources and read the ADC introduction by Jonathan Wall.