I've seen VGA cables for the Xbox 360. You most likely hook it up to display on your monitor. You can still use it as a monitor to display your computer screen, but you'll have to switch back and forth between the two cables.
The only thing that would prevent you from doing this is if you have a older monitor like mine.(it's a CRT monitor). It has the Vga cable preinstalled to the monitor so you can't get it out.
I have an hp m1050y computer with a 19' viewsonic 8ms lcd. Is it possible to hook up an xbox 360 to the computer and play games on the monitor? I still need to use the monitor for the pc, though.