I can answer from my experience....
In the context of Civ4...
Random CTD's
Random reboots of the PC.
General problems that can be seen (these didn't happen to me)
BSOD's
Crashes etc that can't be explained by any other process of elimination
As long as you aren't overclocking your memory, or running it with too fast timings, beyond what it can cope with then memtest86 is pretty good at finding memory problems. Having the correct voltage for the memory is also important.
In my case all of my other games and applications ran fine with zero problems when I had a faulty memory chip. It might have been only Civ4 needing so much memory that used the faulty memory address that was an issue. It took me a little while to test my PC's memory as the machine was otherwise so stable.