Hardware Requirements

The hardware minimum requirements I experienced:

For windowed mode 300x280 low graphics, no texturing:
500 MHz Processor
32 MB OnBoard Graphics
128 MB RAM
(you will get around 9 to 12 FPS)

For fullscreen mode 1024x768 high graphics, mipmap linear mipmap texturing:
1000 MHz Processor
128 MB Graphics Card
256 MB RAM
(you will get up to 70 FPS)

For fullscreen mode 1280x1024 high graphics, m.l.m. texturing, 16x antialiasing:
2000 MHz Processor
256 MB Graphics Card
512 MB RAM
(you will get around 90 FPS)

My current setup:
Fullscreen 1280x1024 high graphics, m.l.m. texturing, antialiasing off:
2x 2400 MHz Processor (Dual Core)
256 MB Graphics Card
2048 MB RAM
(i get 160 to 320 FPS, depends on map complexity)

Conclusion:
BZFlag is mainly CPU bound. A faster CPU will yield better game performance.