ANSWER: Your slim Media Center PC has either a micro-ATX or mini-ITX (SFF) motherboard that provides only a few adapter slots and most graphics cards capable of playing the latest games at 1080p screen resolution and high detail levels are too large for the slim case and they have big cooling units, which means that they take up the space of two slots, so even if you could install one you would probably have to remove the Media Center’s TV card. All Media Center PC’s by definition must have at least one TV card. The term SFF (Small Form Factor) is used to designate motherboards smaller than the ATX and micro-ATX form factors.
The Sapphire Radeon 6670, currently priced at around £75 in January 2012, is a half-height, single-slot graphics card that provides analog VGA and digital DVI and HDMI output ports. It is very quiet, which is what you want in a Media Center PC, and plays Dirt 3 at a very decent 44fps with high-detail and 4x anti-aliasing settings and a screen resolution of 1920×1080.
That was a good example when I first wrote this answer. It’s 2015 now and there are still many half-height graphics cards that you can buy new or used from Amazon or eBay. Just make sure that you get one that is designed for the form-factor of your Media Center PC’s motherboard.
Small Form Factor – http://en.wikipedia.org/wiki/Small_form_factor#SFF_types
