With the original Xbox, i can record by using a USB 2.0 Capture device, i plug in the USB thing in my PC and connect the wires to this http://www.ebay.com/itm/New-Sealed-XBOX-Advanced-AV-Pack-Free-Shipping-/182742688322?hash=item2a8c502242:g:-hoAAOSwJJRZqL76 That only has Svideo. But i don't see anything like that for xbox 360. I only found this http://www.ebay.com/itm/NEW-HDTV-Component-Composite-AV-Cable-for-Microsoft-XBox-360-/191808932479?hash=item2ca8b40a7f:g:8WgAAOSwighZgMtX But i would have to buy something so i can connect the composite to the USB device to the PC.
USB capture card then you could connect xbox 360 composite cables to it....that i think is the cheapest way to do it.