It would be great to be able to start AirDroid on the phone, via a link on a website or a button in a browser. This would let you actually access your phone without having to first physically access your phone.
I'd love to be able to log onto a website, and click a link that would first trigger AirDroid to start on my phone, then present a link to the URL that AirDroid is currently running on. This may be possible to implement using Google's Cloud to Device messaging functionality.
An alternative approach, that is almost as nice, would be to have a Chrome plugin that would let you do the same thing from a button in Chrome's toolbar.
I know it's asking a lot, but AirDroid has already exceeded my expectations, so I am confident the team could achieve it and make their product even more awesome!