If you're a hardcore or even a casual gamer, you should seriously consider replacing your graphics card, especially if you're still using the one that came with your computer. Adding a new video card can greatly improve gaming performance by increasing speed and improving visuals, leading to smoother game play. A better card can enable you to enjoy newer, more graphics-intensive games.
As with any component, you have to look into compatibility. Make sure to pick the right type of card for the slot(s) on your motherboard (either AGP or PCI Express), and one that is physically small enough for your computer case. It is also possible to get too powerful of a drive for your current processor and power supply, which could harm rather than improve your gaming experience. If you have an older machine, it probably can't take the latest and greatest graphics card. A nice midrange card can greatly enhance performance for a couple of hundred dollars, but you can also find much cheaper ones that aren't bleeding-edge that will suit your needs just fine. Some motherboards also support running identical video cards in tandem to boost performance.
An alternative to replacing your video card is overclocking the drive you already have. You can generally do this either with your graphics card's driver or with software tools downloaded from the manufacturer. As long as your computer's cooling fan, the fan on the graphics card itself, and/or your power supply can handle the speed you choose, overclocking should give a modest performance boost. Some negatives are that the noise of your fan might greatly increase, and that overdoing it could reduce the lifespan of the video card. It's worth considering if you are on a tight budget, but improvement is far more dramatic when you replace the card.