How to record a FaceTime call on OS X? How can I record a FaceTime call and save the video on my Mac?

I am using a MacBook Air 11" with OS X 10.8.
There's finally an app for this! Call Recorder for FaceTime is a Mac app that was just released today:

https://www.ecamm.com/mac/callrecorderft/

This product is a plug-in that adds recording controls to the FaceTime app. Recording can be started manually, or it can be configured to record automatically. It creates internet-ready QuickTime movies. 
Another great use is recording phone calls that come through the Mac via Yosemite's new Handoff feature. 

(full disclosure: I work on this product!)