I suggest you to try to record any stream with Replay Media Catcher and WM Recorder before asking a question. Both programs can record streaming audio and video automatically, so the only thing you need to do is launch them and then play your streams. And both programs are free to try.

Most streams these days are HTTP or RTMP flash videos streams. HTTP streams can be recorded by many programs, while there are few programs that support RTMP protocol. Currently Replay Media Catcher is the best RTMP Flash stream recorder (Please note that it can also record HTTP flash video streams including YouTube).