@koshman
My experience is that, depending on the settings I use in a game, additional RAM almost always helps - from the odd loading jerkiness to the ability to keep large textures cached in RAM for longer. However, I grant you it doesn't just make things "faster", instead it helps stop them from getting slower, by mitigating latencies from parts of an application that might otherwise have to go to disk to retrieve something.
EDIT: I completely agree that the game can be more enjoyable with more RAM, but it doesn't technically run faster - if the screen refresh during combat is low, buying more RAM doesn't solve that.
Well, again, that also depends on your settings and quantity of RAM of the "right sort" can make a big difference. Try playing games that use large graphical datasets on identical GPUs but with different amounts of video RAM. Without enough dedicated ram on the graphics card, frame rates can plummet through the floor as data is streamed constantly from system ram into the graphics card.
Now, regarding the Amiga, there is a definite case that adding RAM can improve performance markedly. Just try using any 68020+ with Chip RAM only
