Be sure to check the support article section related to the game you're having problems with. There you can also find troubleshooting threads which our users have found helpful.
It's important that you have the latest version of DirectX and graphics drivers installed!
If you're using Windows Vista or 7, you should try disabling UAC. More information can be found here.
Installing the latest updates for your operating system is always a good idea and can also resolve some of your issues. Same thing goes for shutting down or disabling any non-crucial applications running in the background, especially anti-virus software, as they might interfere with your games. Try it and see if it helps.