FFmpeg is a free and open source software library and the best solution to record, convert and stream audio/video files. The tools and plugins it contains can easily convert a video file from one format to another. It is the most important component to run a video sharing website. It can easily fetch audios/videos from a live source.
FFmpeg is developed under GNU/Linux, but it can be compiled under most operating systems, including Mac OS X, Microsoft Windows, AmigaOS and MorphOS.