Graphics cards can be troublesome in Linux. Integrated graphics cards such as those made by Intel are usually OK nowadays, but the kind of cards seen on more high-end machines can be more troublesome.
Fortunately, there's a great tool to help with ATI and Nvidia cards, called Envy. This is a set of scripts designed to detect your graphics card, install the correct driver for you and configure the X window server for you. So, if you have any problems with a graphics card from either of those two manufacturers, Envy should be your first port of call (if not, the Ubuntu Forums are your best bet). For those of you running Linux Mint, Envy is preinstalled.
There may still be cards that people can't get working, but Envy goes a long way in making it easier to get your card working right.