Generally, no. Most games are meant to run in Windows only, and Mac compatibility is given little thought. Some games are made with Mac functionality in mind, thought, such as The Sims 3. You'll need to check the box of any game you want to play to ensure Mac compatibility before you open the game.
If your Mac has a copy of Windows installed through Bootcamp, you should be able to run most PC games that way. You'll still need to check your Mac's hardware requirements to make sure your Mac can provide what the PC game needs. You can use Can You Run It? to help determine if your Mac running Windows meets the game's requirements.
Hope that helps!
