Memtest86 is a RAM diagnostic program for x86 computers, by Chris Brady. Its intent is to check memory very thoroughly (better than BIOS memory checks, anyway), and provides various tests. It can also generate BadMEM parameters so the OSes can avoid using bad memory.
It's distributed under GPL.
It doesn't require an operating system, as it's supplied as a bootable image file; you can write it on floppy and boot off that, or use your favorite bootloader.
(As a funny sidenote, file(1) command identifies memtest86 boot image as "Linux kernel from prehistoric times".)
The home page, as of writing: http://www.memtest86.com/ - (here come the legendary words) it's also available as a Debian package.