Mountain Lion: how to change webcam resolution
Apple (or a 3rd party) should write a utility to allow you to dial down the native resolution of the internal camera, but to my knowledge they have not, so far.

You can work around this by piping the video output from your web camera into another program that processes the camera's video stream and "re-publishes" it to your Mac as a virtual camera (aka pseudo-camera) which will be available for use in other applications on your Mac.



Here's how I did it. I've tested this solution under OS X 10.8. It also works under OS X 10.6. (I'd bet it probably works in 10.7, also.)


Download the free (donation-ware) webcam effects utility CamTwist Studio.
Set your web browser to run in 32-bit mode.  (Why? Because the Adobe Flash  browser plugin must run in 32-bit mode in order to access the CamTwist virtual camera device.)  To do this, go to the Finder, locate your web browser app, do "Get Info", and check the "Open in 32-bit mode" checkbox. Don't launch your web browser yet.





Open CamTwist Studio, go to the Preferences, click the Video Devices tab, choose your video device, then use the "Force camera resolution" setting to force whatever resolution you prefer. (Suggest 320 x 240 for low-bandwidth internet connections.)





You'll then need to define a "Setup" in CamTwist studio. Follow the Steps in the CamTwist main window: double-click "WebCam" from the Video Sources column. 





Skip to Step 5 in the Cam Twist main window - select your camera device in the Settings column:





Open the Preview from the Tools menu. A window should pop up showing you a live video stream from your camera device.
(optional) If you wish, play around with the many interesting effects available within CamTwist, such as "Comic Book," shown here:





Now you're ready to launch your web browser (in 32-bit mode). Most web-based video chat/meeeting services (such as GoToMeeting) use Adobe Flash for handling video. When you go to configure your camera settings for video chat, you should see a new "camera" device available, called "CamTwist Studio."  If you select this device, your video stream should be the modified, low-resolution 320x240 (or whatever size you chose) stream, plus any effects you added in CamTwist.


The CamTwist "virtual" video device should also be available in most other programs that use Mac OS X Core Video services, i.e. Skype and many other apps. (But not all. For example, it doesn't work with FaceTime.)

Here's an example of the CamTwist video stream being used on http://www.chatroulette.com: