Mine would be the headset, the one that comes with the system is okay but you quickly grow out of it. I ended up shopping around a good bit before I found one that actually worked well enough to my standards and had an extra long cord.
I think that if I had a Kinect, that it would be my favorite accessory. Since I don't have one, I'll go with the headset we have. It's not the cheap headset that's included with the system - it's one of those Turtle Beach bad boys.
Aside from my controller, I don't have any Xbox accessories, so I guess my favorite accessory is the controller, ha ha! Seriously though, I do like the 360 controllers better than the controllers for other consoles, especially PS. Xbox 360 controllers are larger and more comfortable.