It is very hard to get access to useful information on recent graphic chips. However, it is possible to learn a lot from existing old graphic chips and information about them is often easier to find:

• VGA/SVGA information.

Intel

• intel 740: gives a functional overview of the 2d/3d graphics engine as well as the video out engines (datasheet).
• intel 82815: functional overview, detailed programming interface.
• intel 82845G with Extreme Graphics technology.
• intel 82865 with Extreme Graphics 2 technology.

Chips & Technologies

Intel bought them a while ago and discontinued their products. However, technical documentation is still available from the Intel website there. These are really old 2D-only graphic cards.

• 65548 datasheet.
• 65535 datasheet.
• 65510 datasheet.

Via

Via designs low-cost x86 clones and chipsets. Some of these have 2D and 3D support:

• Apollo PLE133 chipset datasheet: contains the register description and the operational description of the 2D and 3D engines.

3Dfx

• Register specifications for Voodoo 1/2/3/Banshee/Rush chips. I believe these datasheets were freely available from the 3Dfx website before they were bought by NVidia. The copyright mention in each of these datasheet mentions that it is okay to redistribute them.
• Glide programming guide: a bit of information on the architecture of 3dfx cards/chips.

Silicon Motion

• SM 501: (the datasheet) a 2D mobile chip.
• SM 712: (the datasheet) a 2D dual-head mobile chip.
• SM 722: (the datasheet) a 2d/3d chip.
• SM 731: (the datasheet) a low-power 2d/3d chip.