What depends most in a case to fit a graphic card?

Solution
on cases now there are two types. gaming and non gaming cases. the non gaming cases when you look at photo of them have the hard drive bay facing the back of the case looking at the power supply this limits the lenth of the gpu thta can be added.
http://watercoolingcase.computer-parts-store.com/images/Nine_Hundred_Black_Steel_Atx_Mid_Tower_3_large.jpg
gaming cases now have the drive bays facing the outside door of the case and can be removed or are installed lower then the video card slots.
http://images10.newegg.com/BizIntell/item/11/124/11-124-162/s0_100314.jpg
on cases now there are two types. gaming and non gaming cases. the non gaming cases when you look at photo of them have the hard drive bay facing the back of the case looking at the power supply this limits the lenth of the gpu thta can be added.
http://watercoolingcase.computer-parts-store.com/images/Nine_Hundred_Black_Steel_Atx_Mid_Tower_3_large.jpg
gaming cases now have the drive bays facing the outside door of the case and can be removed or are installed lower then the video card slots.
http://images10.newegg.com/BizIntell/item/11/124/11-124-162/s0_100314.jpg
 
Solution
What depends most is the case itself..
Different cases support different depth graphics card. You need to look at specs of your card you want and specs of your case and match them (sometime you will have to google to get mm to inch conversion).

As smorizio was pointing out, hard drive orientation can make things simple or a huge pain.
While it is perfectly possible to put your hard drive in, and have your GPU just barley not touching your hard drive in a front-to-back facing hard drive tray; this means you will have to remove your GPU (and possibly other items) out to remove a hard drive. Any case I buy I make sure it has side-to-side hard drive tray, and not front-to-back facing tray because it makes life so much easier.