I have had a lot of experience with AMD products. I go back to the ATi Radeon X300 SE, which if my memory serves me right was one of the first PCI Express x16 GPUs. I have had a lot of experience with Linux as well, starting a year or two after the X300 SE. More recently, I have had experience with OpenGL programming. The current systems I have with AMD products are:

Dell Dimension 8400 (with the mentioned ATi Radeon X300 SE)
HP Pavilion dv6-6135dx (AMD A8-3500M APU which contains AMD Radeon HD 6620G GPU and also has a dedicated AMD Radeon HD 6750M GPU for Switchable and/or Dual Graphics)
HP Envy m6-1205dx (AMD A10-4600M APU which contains AMD Radeon HD 7660G GPU)

and I have had a few other AMD laptops. I have helped pick out for others or purchase for myself a total of 6 all-AMD laptops since October 2009 and I haven't had an issue with them nor have the ones I helped pick out.

The main reason I go with AMD is the price to performance ratio, or "bang for your buck." For example, I picked up that HP Pavilion dv6-6135dx for $699, and that was bought the day it was released. To get an Intel system with comparable performance at that time, I would've had to spend at least double that amount. The system is also completely overclockable (CPU and both GPUs if you know what you're doing), even on Linux with a bit of programming and Linux kernel knowledge (it can't be overclocked via BIOS settings, it is overclocked via software). I'm able to run new release games with 90% of the bells and whistles turned on and have a playable framerate (40+ FPS).

Now, I'll get into OpenGL and driver stuff. This is the stuff I see a lot of people complaining about around here.

General Driver Complaints:
- Doesn't support new X or Linux Kernel releases:
If your Linux distro is using a new X or Linux Kernel release it is their responsibility to patch the driver to function on them properly. AMD doesn't rush officially supporting these newer releases because they take the time to ensure that there is no drop in driver performance or compatibility or other issues brought up by these new releases. They want to make sure the product they are putting their name on doesn't have those issues. I myself use Kubuntu 13.04 for Linux, and I use the xorg-edgers PPA repository which recently has had the fglrx packages updated quickly after new releases. They have them patched to support the newer Linux kernels and X releases. It works without a hitch on both of my aformentioned AMD laptops.

- Poor 2D performance:
This has been 100% resolved since the 12.6 release of the drivers.

Have you filed a bug report, including proper stack traces? Without doing this, there is no way for AMD to fix the issue.

Nvidia's implementation of OpenGL is not to proper specifications. Application developers using Nvidia can end up having issues with AMD users because AMD properly implements OpenGL to the actual specifications, so the developer is using this non-standard OpenGL and expecting it to work everywhere. Complain to your developer and/or Nvidia. In my experience with OpenGL programming, I've ran into issues with Nvidia users because their OpenGL implementation doesn't behave properly! I'm forced to then check if a user is using an Nvidia GPU, and if so, having to use hackish workarounds or even disabling certain features for them. I have to do this for Intel as well, but not as often as I have had to in the past. Intel has definitely come a long way with GPUs recently and I applaud their efforts. Competition is good for everybody.

Specific Driver Complaints:
- Cannot resume from sleep:
I have issues resuming from sleep when using the open-source radeon driver. When I install fglrx these issues go away. This has been reproduced on at least 3 AMD systems I've worked with so I have a hard time believing the people mention this are really being truthful or actually using fglrx.

If you have other issues you'd like to bring up, I'll offer a rebuttal. This is only what I can think of at the time, I just can't stand to read another thread page full of trolling AMD on this forum. Even the articles themselves are biased here!