Usually, when a computer is really slow playing games, it's because it's graphics card is not powerful enough. If the problems is on 3D games, and want better performance, you'll probably need to get a new one...
If its a PC then its probably the older technology and your motherboard probably wont support the newer cards, however you should still be able to upgrade to 128MB - 256MB which will run some games however again not new ones.
If you have a laptop your out of luck. Laptops have everything soldered to the motherboard to fit everything in.