A great article on building the cheapest and best PC possible. The total price? $525.46 with LCD and $461.02 with CRT. That's less expensive than a stripped down Mac mini and better than a low-end Dell.
What did they pick? An AMD Sempron 2800+, 512MB of memory, on-board sound and video, and a $178 Acer LCD monitor. Powerful? Sure. Cheap? Hell yeah.
Ars System Guide: Ultimate Budget Box [ArsTechnica]