If you have a game system and want to play it using a computer monitor, then you need a converter to change your TV signal into a computer monitor signal. These two signals are completely different, and cannot be passed through without a converter.
One such device is called "Xpert TV". This converter takes in traditional TV signals from PS2, XBox, GameCube, VCRs, DVDs, you name it. It creates an output signal that your computer monitor can understand.
This conversion isn't cheap - it is around $100 for the converter unit. In my book, I'd rather just buy a cheap TV for the $100 vs the converter box. But yes, if you have a very high quality monitor, then the resolution you get on that screen at 1280x1024 is going to be better than you can get from normal TV screens.
The games won't suddenly become "more clear". The game can only output at whatever resolution it is programmed to be at. However, if you then use your high resolution computer for DVD playing, you will see a noticeable improvement in your picture!
Xpert TV to VGA from PCMall