Just to show it can be done, this is Turbo, a no-name 120Mhz Pentium 1 desktop with 48Mb memory and a 1.5Gb hard drive. Turbo is sporting a fresh-brewed copy of Ubuntu 6.06.1, with an exceedingly sparse XFCE desktop installed.
Video is courtesy of an ATI Mach64 PCI video card. I pulled the sound card, the SCSI adapter and the modem (all ISA cards) just to keep things as clean and simple as possible. The NIC is an ancient Intel Ethernet PRO 100 pulled from the carcass of a Compaq desktop.
Installation took about six hours, with four of that going to hardware troubleshooting (it's a new-to-me machine). Only two or so went to the necessary tweaks and adjustments to keep Turbo in a manageable state. Turbo is running the stock Ubuntu 2.6.15-26-386 kernel (the 686 drove him batty -- but I had to try it) and a 16-bit desktop at 1024x768.
The only real problem is that Turbo's only mouse connection is via serial port. And I don't have a proper serial mouse (my adapters don't seem to work), so I'm mouseless. Which makes things a little difficult to use. ...