Can you play PC games without the game

Firstly, you need to have purchased, downloaded, or otherwise have access to the game. Most games are designed so that they ask for the disc each and every time you play. This is a way of making sure you did not just download some hacked version off of an unofficial internet site, which would be piracy.

As far as can you...
Technically, the answer is yes. Many gamers do not like to bring their disc out everyday, and put it at risk for damage. They download serial cracks so that they no longer need to. Just keep in mind that doing so is going to be a violation of your service agreement, and if it is an online game, they can likely detect it has been cracked, and toss you off.