There is a new distribution based on Ubuntu under development which is called Ubuntu Lite. The idea of Ubuntu Lite is to bring the power of Ubuntu across to the users of legacy systems.
So not just to make a small linux as this has been done before (Puppy Linux, Damn Small linux, the Rule Project). Nor to make a usable linux based desktop Operating system (that has been done with Ubuntu Linux, Beatrix). The idea is to bring the power of Ubuntu to the typical users of legacy hardware.

There are three core aims of the Ubuntu Lite Project:

1. easily used by people with minimal computer skills
2. usable on a resurrected system
3. able to satisfy a typical users requirement of applications and functionality

If you run older computer hardware, just give it a try!