It depends.
Typically it is not possible to do this because most monitors do not have the proper connections to accomodate standard video devices (they only have computer-centric VGA or DVI cables). However, some recent large LCD monitors do have standard video inputs like composite or component.
If yours has a composite, then there is no problem. I am guessing this isn't the case as you would have figured it out already and never posted
If it has an S-video, then you'd need that cable.
If it has a component video input, you'd need that cable, plus an early-model gamecube which had the digital-out connection.
Otherwise you will need to get a device which can take video inputs like composite or S-video and output them as RGB VGA signals for a regular monitor. They exist, but are expensive (I guess at least $100 for a decent one). Unless you are
very tight on space it is usually not an economical choice to use these devices.
Otherwise, you're short of luck as far as I can tell.
Ruahrc