There are so many cool ways to record
xbox 360 gameplay. I have 2 ps3 and an xbox elite. o, and a wii and i record from all of them.
You can use virtually anything to record video games:
The original question was how to record without a capture card, "I want to record my xbox 360 gameplay, but without having to buy a capture card".
Pick your poison according to the quality of the resolution you want to get. That should get you started.
It is clear that not all gamers want to record video games with a computer near by. Anyways gamers are always looking for a quicker and better solution to solve complex problems. And making a hd pvr (vs. a capture card) eliminates a large part of the overhead.