It costs some money but for the Xbox this adapter works great. Only games that won't work are the few that were released with only 480i support.http://www.x2vga.com/
I've got one and love it. I know there were a few others that frequented GoneGold that had one also, and from all I heard they had nothing bad to say about them.
If you're curious what games support at least 480p (needed for using a monitor) check out HDTV Arcade
for a list.
ALso be aware that with the X2VGA you can not use your XBox as a DVD player, since it does not support progressive scan for movies.