Memtest86+

Memtest86 is a tool for testing system RAM. It runs a number of increasingly-subtle tests to determine whether your RAM has errors. It is an oft-overlooked tool that has helped me diagnose hardware issues many times over.

Memtest86+ is a fork of the code which added support for larger memory sizes and newer processors. Unlike the original version I was able to find a donations page for the forked version, so that is my nominee.