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.
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Facetime does not include this functionality directly.
One of the possibilities you have is using QuickTime X's screen recording feature.
There's finally an app for this! Call Recorder for FaceTime is a Mac app that was just released today:
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!)