Many people now use Facebook to keep in touch and share information with friends. One of the features used the most I believe is the fact that you can create a photo gallery and upload any number of pictures to it. Thing is, you upload the photos using a Java Applet!
That's probably the only mainstream use of a Java Applet I've ever seen. But sometimes it doesn't work, not even for me, sometimes it just doesn't load on my home PC. Its happened to my brother and to several of my friends as well and they've all come to me for help. Usually it involves re-installing the JRE in order for it to work again as I recall.
So in playing with AIR allot lately, it would seem like a perfect use of the technology. That is what AIR was built for afterall, to allow end-users to interact with their desktops and the web at the same time. In this case the AIR application would allow an user to browse his local pictures and select the ones he wants to include in the photo album (with a preview). Finally he would upload them to his photo album for all of his friends to see. Advantage here is that the download/install process would be easier for end-users (smaller download) and would hopefully be more robust and work 100% of the time.