You can download or capture streaming videos using streaming video recorders. They either download streams or capture packets from streaming media players.

If you want to record video from screen, you need your window to be on top to be able to use screen recorders. Replay Video Capture and WM Recorder allow you to bring the Windows on top so that you can work while the video is being recorded.

Let me know if you find any programs that can record from screen from windows that are in the background.