Quick update for Ubuntu users: FFmpeg isn't available in recent Ubuntu releases but that will change with Ubuntu 15.04 Vivid Vervet (currently under development, to be released in April, 2015).
FFmpeg is a free software project that produces libraries and programs for handling multimedia data. Due to conflicts in the FFmpeg community, FFmpeg was forked back in 2011 and the resulting project was Libav.
Since then, various Libav changes were merged back into FFmpeg, while Libav did its own development, ignoring any changes from FFmpeg, and as a consequence, many developers prefer FFmpeg. For more information, see these pages: 1 2.
Ubuntu replaced FFmpeg with Libav a while back - for instance, Ubuntu 14.04 and 14.10 have only Libav -, but there's some great news for those who prefer FFmpeg: with Ubuntu 15.04 Vivid Vervet, FFMpeg returns to the official Ubuntu repositories.
Ubuntu 15.04 Vivid Vervet currently has FFMpeg 2.4.3 (imported from Debian) and because both Libav and FFmpeg use the same library names, the new FFmpeg package ships with renamed libraries, like "libavdevice-ffmpeg", "libavutil-ffmpeg" and so on, so the packages can coexist in the Ubuntu (and Debian) repositories.