MemTest86+ Tests Memory for Free
I've been using Memtest86 and its successor Memtest86+ for so long now, it's hard to remember when I started; a decade ago to be sure. Memtest86+, as you might guess from the moniker, is a memory checking program that runs a battery of memory tests including random numbers, moving inversions, bulk writes, etc. What you might not guess is that it's free/donationware.
Memtest86+ boots and runs automatically. It continues running until you stop it, so it's highly useful for CPU and memory burn-ins, as well as spotting memory problems that only show up after a system has heated up. The interface, if it could be called such (you don't interface with it except to quit, and you may end it by simply turning off your PC) is character-based (DOS-like) and tells you everything you need to know. If you see red, your memory has problems; otherwise your memory is fine.
I've used Memtest86+ on literally hundreds of PCs, both for memory and CPU burn-in and tracking down memory issues (which generally present themselves mysteriously as blue screens and random lockups). It's never failed to find a memory problem. It even shows you the problem addresses so you can determine which module is at fault.
Memtest86+ downloads as a 70KB zip file that expands to about a 2MB .iso and no, that's not a typo--it's lightweight and then some. Burn it to CD, boot it, watch it, and that's it. There's also a version for floppy and one that will install on a USB thumb drive--both equally as small.
Memtest86+ is so useful, it's even included on the Parted Magic and Slax Linux boot discs to troubleshoot what might appear to be installation issues. It's an absolute must-have for any PC toolbox. The team accepts donations so throw a couple of bucks their way if you get a chance.