Real answer given in the game? The vast majority of them just sleep. Some of them are more active and scour the galaxy, keeping tabs on the various civilizations, learning about their strengths/weaknesses, enslaving agents and making sure that organics don't grow too powerful. Some might be involved with managing various "slave" races like the Collectors. But the game explicitly says that the vast majority of them simply go to deep space and enter a hibernation mode to conserve energy and prevent them from being accidentally discovered. So, yeah, they merely wait and rest up for the next harvest.
Again, that might seem confusing: why do they do this? What purpose IS there to their existence if ALL THEY DO is kill, go back to sleep, wake up, kill, go back to sleep, wake up, kill ad infinitum? Well, the Reapers say that their true purpose is apparently "beyond" the understanding of Organic life forms. ME2 hints that part of the harvest is to reproduce and replace lost reapers (every once in a while one of them does die). But until ME3, we'll don't know why they seem to be content to exist in a seemingly pointless cycle of "Kill, sleep, kill, sleep, kill some more, then sleep some more". It's entirely possible that they wait for organic civilization to grow, assess new species, technologies, cultures, and then before they can grow too powerful, wipe out the ones they don't like and forcibly incorporate the ones they do like.
