XUbuntu or smaller
You'll need to check the hardware minimum requirements for distros. In Ubuntu's case, you'd certainly load XUbuntu, not regular Ubuntu, which requires 512MB RAM minimum. There are also stripped down versions of Ubuntu and other distros for older systems. Cloudbook, a new laptop coming out soon, uses a smaller version based on Ubuntu. Asus' EEE PC uses another small Linux version. Offhand, I don't know the names of these.