I've always gone with an Nvidia card, and they've treated me well and i've gotten great use from them. However, i recently bought an AMD card for a great price, so it'll be interesting to see how it goes for me.
I like NVIDIA, AMD, and Intel. Intel is good for when you just need graphics. Nothing super fancy, though the Intel HD 4600 and 5200 are supposed to be decent. NVIDIA is good for when you want power, but cost isn't a super big issue. AMD is also good for power, but when cost is somewhat important. Also, NVIDIA I find best for laptops, since THEIR Graphics-Switching solution is much better than AMD's. NVIDIA is also decent for Linux. I haven't had any issues getting an NVIDIA card working on Linux, while I have had issues getting an AMD card working.