The Answer: LICEcap

LICEcap is a tiny, free open-source application for Mac OS and Windows that makes it insanely easy to record any portion of your screen. I use it all the time to provide people with short (3-10 sec) instructional screencasts and walk-throughs.

LICEcap Screencast GIF Recorder Demo

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LICEcap can also record in a lossless, higher quality format (.lcf).

In addition to .GIF, LICEcap supports its own native lossless .LCF file format, which allows for higher compression ratios than .GIF, higher quality (more than 256 colors per frame), and more accurate timestamping. If you record to .LCF, you can play back the .LCF files within REAPER (and/or use it to convert to .gif or another video format).

More information is available at cockos.com/licecap.