I‘ve already dealt with different cables and their quality, and now I would just like to give you a few important notes on connecting your XBOX to a TV of any kind (CRT, Plasma, LCD, LED, etc).
What your TV needs
Your television set needs to be able to display either the 480i (NTSC) or the 576i (PAL) video modes. The more native XBOX-resolutions your TV can display (480i, 480p, 576i, 576p, 720p and 1080i), the better!
Your TV also needs either a composite, SCART or component input, preferably the component one as it gives you the best visual quality. Also, to receive sound the TV needs to include a composite audio input (this is included in a composite input).
What your XBOX needs
To take advantage of the best video quality and the highest HD-resolutions, you will need to purchase a component-cable for your XBOX. These are usually pretty cheap and come with a separate composite audio-cable.
If you have an older TV without support for HD-resolutions, you might be better off with the standard XBOX to composite cable.