Take Ubuntu. Rip out the Unity user interface and drop in LXDE (aka the "Lightweight X11 Desktop Environment"). This frees up resources (both memory and CPU) and generally makes your systems a bit snappier.
Then take out LibreOffice and Firefox. Sub in Abiword, Gnumeric and Chromium. Lightweight, super-face office suite and web browser? Check.
Those sorts of tweaks, and software swaps, are common throughout the system — and almost invariably resulting in a system that is just that much leaner and peppier. They even opt to use Sylpheed for the email client (instead of the common Thunderbird). Seriously. Sylpheed. Who uses Sylpheed? Well, apparently people who want their systems to be crazy fast and stable.
In many ways, Lubuntu reminds me of Ubuntu of old — back when Gnome 2 was the bee’s knee’s. Lubuntu even comes packed with Synaptic Package Manager (the old graphical software installer from versions of Ubuntu more than a few years back) and full access to all of Ubuntu’s software repositories (it is an Ubuntu-derived system, after all, with close ties to the Ubuntu release cycle).