Memtest86 is thorough, stand alone Memory test for x86 architecture computers. BIOS based memory tests are a quick, cursory check and often miss many of the failures that are detected by Memtest86.
Memtest86 was developed by Chris Brady with a first release in 1994. However, the testing algorithms used have been under development since 1981 and have been previously implemented on Dec PDP-11, VAX-11/780 and Cray XMP architectures. Development and distribution of Memtest86 is now funded and supported by BradyTech Inc.