I've put Windows 7 on two older PCs:
P4A (533 MHz FSB Prescott, Socket 478) 2.8 GHz, Geforce FX5200, 768 MB RAM
Celeron (400 MHz FSB Willamette) 1.7 GHz, Integrated Graphics, 1.125 MB RAM
The former has absolutely no problems, even if Aero is running. I'm sure serious multitasking could give it trouble, but it's fine otherwise.
The second runs well with all of the eye canding disabled. The integrated graphics, unfortunately, push the processor a bit further than it would like to go. I'd put a dedicated PCI GPU in it if I knew one with low power requirements. I tried to put a PCI 8400 GS (or something of the sort; cheap nVidia PCI card), and it would POST, but failed to boot.
I've installed Windows 7 on a Duron 800M with 512 MB RAM and integrated video before, but I didn't attempt to run it. I have a feeling that it would run fine if it wasn't for the integrated video.
Why do people assume Windows 7 is very demanding? Anyone have any ideas on a low-power video card for the Celeron?