I installed XCom a while ago and something horrible happened. When I changed my point of view by pressing the Q button, and then I move one of my soldiers, my screen froze and I had to force-shut-it-down in order to allow it to recover. I have been using this same computer for the past year and this never happened before.
Sounds like a problem with your graphics card. What graphic card does your computer have?
Try to install the most up to date graphic driver, that may solve the problem