Everyone knows that in general, Nvidia has the best supported graphics cards under Linux. But I don't want to buy into Nvidia's proprietary drivers if I don't have to. ATI has open source drivers, but they have almost no support, and their open source drivers are significantly worse than their closed source drivers. Intel has open source drivers, but their graphics are all integrated and built into the motherboard.
Are there any graphics card manufacturers which have open source drivers and are actually friendly with the open source community? I would gladly like to purchase from them if they exist.
The answer is a little complicated, but goes like this:
Nvidia's open-source driver is really bad (thanks to them being stubborn), but their proprietary driver gives pretty much the best performance of any GPU on Linux.
AMD's open-source driver is better, but still not really good enough to match your investment in a modern video card, so you'll end up resorting to their proprietary driver, which is not as good as Nvidia's.
So: if you're serious about wanting to go entirely open-source, AMD is a slightly better option (though still dissatisfying -- honestly, Intel graphics are probably the only ones whose open-source driver compares well to their Windows performance nowadays, and that wasn't true until 2012), but if you're willing to use proprietary drivers, Nvidia is best.
Note that this assumes that you're using <5 year old hardware, willing to spend north of $100 on your GPU, and have some interest in modern games.
There are only three competitors in the GPU market that play a significant role and you just named them all. Sadly, the answer is no.
You can check out these two:
Intel integrated graphics card on new motherboards have good performances and open source drivers. Except for the fact that they are integrated, they are a good option.
More general discussion on the wikipedia page: http://en.wikipedia.org/wiki/Graphics_hardware_and_FOSS.
See also this strongly related question Open source graphics card options?