Make mine a Lite, a MEPISLite
MEPISLite 3.3.1-2, a late beta version, is designed from the ground-up to be a fully functional Linux system that will run on a Windows 98 class machine. It is reported to run on as little as a Pentium II system with 128MB of RAM and a 2GB hard drive.
I believe it.
There are, of course, many other small Linux distributions. Zenwalk (formerly Minislack), Puppy Linux, and Damn Small Linux, to name a few. All have their fans.
Still, I think MEPISLite deserves anyone's attention.
For starters, it is a complete desktop Linux system. You're not going to sit down at MEPISLite and find yourself wishing for functionality that's not there.