There are different types of games you can play on the computer. Some can slow down your computer but other games can not slow your computer down. Online games for example do not needlessly use much of your computer resources. Whenever you play a game online, most of the game functions are processed within the web browser (such as Firefox and internet explorer).
Playing games online will not really slow down your computer because web browser will be responsible for the games animations and sound. If you have decent amount of memory to process sound and animation then your browser will be able to handle online games.
On the other hand if you play games on your computer that is locally installed on your hard disk then your computer may slow down. Some games are memory and CPU intensive. What this means is that some games need huge amount of memory in order to load, and once they are loaded they require CPU to constantly run large and difficult processes in order to enjoy the game.
If you play games on your computer then you need a gaming machine. Desktop computers are best for gaming. Some desktop computers are designed with gamers in mind. You get high-end CPU, memory and graphic cards in order to enjoy your games.
If games slow down your computer I suggest you upgrade your computer's components, and the best CPU for gamers is the Intel Quad Core which has 4 cores in 1 CPU. You may also want to get additional memory and better graphics card for better animation.