MemTest-86 is a simple but thorough tool which will scan your PC's RAM for errors. It's been around for almost 20 years, but is still being updated to fix bugs and ensure it works with the latest hardware (which includes both 32 and 64-bit systems, so don't be concerned about the "86").
The program comes in the form of an ISO image, so it's not quite as convenient to use as some of the competition. You'll need to use another program to burn MemTest-86 to disc (or create a bootable USB key) before it's ready for use. But once you have made those preparations, everything else works very well.
MemTest-86 boots immediately, for instance. There's no complicated operating system which needs to fire up, first - you're straight into the program's simple text-based interface. A menu offers a selection of test options, but you don't even have to worry about that: just wait a few seconds and the default test pattern will begin.
The screen then updates to show you exactly what's going on, the various tests that are being used. It's fairly technical, but if nothing else the "Pass %" and "Test %" will show you how far through the checks you are. And again, there are a lot of error types which could be reported at the end of the test (MemTest-86 is very thorough and detailed), but you don't really have to understand those, either. If you see any errors, there's a problem with your hardware; if you don't, your issues are probably somewhere else.
Version 7.1 (Version History):
Fixed a bug in measuring CPU clock speed using HPET which could skew the clock speed results to unreasonable values. This may have caused issues during startup including extremely long loading times
Added fallback mechanism to use the legacy PIT to measure the clock speed if the measured CPU clock speed using HPET is unreasonable
Disabled code optimization for Test 12 due to reported freeze when running in parallel mode
Fixed CPU selection mode not being set according to the results of the multiprocessor test during startup
When switching to the next target CPU in Sequential/Round Robin mode, attempt to reset the target CPU if there was a failed attempt to switch the BSP
When looking for SMBus devices for RAM SPD retrieval, attempt to look for any disabled SMBus devices to enable before enumerating the PCI bus
Fixed cursor appearing for some systems during testing
A thorough and reliable way to check your system for RAM issues