I have purchased (second hand, cheap) an HP Pavilion 753n desktop, for the kids. It was all I could get my wife to spend.
My kids are young 9 and 6, so the games that they would like to play aren't too 'sophisticated', yet. Most of the games I have installed have worked, except for Sonic Heroes and Lego Star Wars.
The onboard graphics are lacking, and I'm looking for a AGP 4X video card that will work, and not require a power supply upgrade also.
The 753n has an AGP 4X slot on an MSI MS-6577 Rev 1 mbo with an Intel i845G Northbridge chipset. I'm not sure of the power supply, it's either 250 or 300 watts. I'm also adding another 512MB of RAM for 1 Gig total, which is max.