For those NVIDIA GeForce and ATI/AMD Radeon users using the vendor's respective proprietary Linux drivers, there shouldn't be any issue in handling Doom 3 / id Tech 4. On the ATI side I remember running Doom 3 easily on a Radeon X800XL 256MB back in the day along with a GeForce 6600GT on the NVIDIA side. With the current Catalyst driver only supporting the Radeon HD 2000 series and newer, anything that is running with the Catalyst driver in 2011 should be able to run Doom 3. On the NVIDIA side, their mainline binary driver supports the GeForce 6 series and newer, so there you should be set too. Any modern graphics card with the proprietary Linux drivers will likely be CPU-bound. The binary drivers deliver Doom 3 results that are much faster and more visually advanced than what is illustrated in this article, so the binary drivers are not the focus of this article.
First to be tested was the integrated Intel HD 3000 graphics from the Core i5 Sandy Bridge. While Intel has had seven years to advance their Linux graphics driver since the release of Doom 3, the latest Mesa driver code still is not perfect. Running Doom 3 in a stock driver configuration for the Intel Linux graphics under Sandy Bridge caused issues. There were multiple times where the system would hang and there would be visible memory corruption to varying extents.
There were also times there would not be frame-buffer corruption, but the Sandy Bridge graphics processor would be hung and then restarted by Intel's DRM kernel driver (as reported by dmesg). Sometimes there would be the GPU being hung twice, which was not gracefully recovered.
In the end, however, I did manage to get some Sandy Bridge performance numbers from Doom 3 on the Linux 3.2 kernel and with Mesa 7.12-devel.