Minecraft wiki entry for Videos, associated text: FFmpeg (Linux, Mac, Windows)
FFmpeg is a bundle of command line tools and libraries. Recommended only for advanced users.
Some libraries may be patent-encumbered - see FFmpeg's Legal FAQ
Open Broadcaster Software (OBS Studio) (Linux, Mac, Windows)
Screenflow (Mac Only, Commercial)
SimpleScreenRecorder (Linux)
VLC Media Player (Linux, Mac, Windows)
Note: Capture and Streaming are not the primary purposes of VLC. Captures are in a lossless AVI format, and as a result can quickly fill up storage space. Transcoding is highly recommended.
Xsplit Gamecaster (Windows, Commercial)
and many more!