How do I take video clips of my activity on the XBox 360?
The Roxio Video Capture USB and Dazzle Video Capture devices allow you to redirect the RGB output from video game consoles to a computer.
This product from Blackmagic Design seems to record RGB, audio output, S-Video, and HDMI.
From there, you can record your PC screen, either with drivers from the companies of the products or with alternative screen-recording software.
(Note: These solutions cost money to buy the products, but work for any devices that output via the formats listed.)