Microsoft shipped the original Xbox with a composite AV cable, which was fine for 2001, but composite doesn't work very well with modern HDTVs. You could buy a component cable for your system, but official Microsoft cables are hard to find and expensive. Not all HDTVs even have support for component either. If only the original Xbox had an HDMI port. This post outlines the process of adding an HDMI port to the original Xbox.
Things you'll need
Here's a list of items that you'll need for adding an HDMI port to the original Xbox.