Graphics cards + CPU combinations

Do you get more performance out of an AMD graphics card if you use an AMD CPU rather than an Intel CPU? If so, what makes it more suitable?

No, you don't. Right now, if you have the money, the sweet spot configuration is an i5-3570K with a Radeon HD 7970( they're not both AMD, you see).

Likewise, I have been using AMD CPUs and NVidia GPUs since the Athlon XP 64 (single core). Never had any issue.