***SPOILERS! SPOILERS! SPOILERS! PLAY ME3 FIRST!***
I came up with my own theory of what drives the Reapers, because everything Casper says is nonsensical bull****. I'd still prefer that they allowed the reapers and their motives to be an incomprehensible mystery, but unlike Casper's explanation, my theory would actually account for Shepard and others being able to understand them. Anyway, this is just for fun, but here goes...
Mass Effect has always had a somewhat biblical theme, right? Or at least it references the Bible here and there. In many ways, the reapers can be compared to the Christian god; no creator, no beginning or end, unfathomable realm, omniscience, indoctrination, purging civilizations, harbingers, messengers, disciples - *many* ways. Well, let's look at some of thing things God is famous for doing. He banished Lucifer and all of his followers from Heaven because they would not obey him and demanded to be his equals. They even conspired and took up arms against him. Then God condemned Adam and Eve for eating the "fruit of knowledge." Knowledge is power, power enables ascension. With enough knowledge, one could begin to question God. And with enough power, one could eventually challenge him. Then there's the Tower of Babel...
The tower of Babel was supposedly man's attempt to come together and build this structure to reach Heaven and see the face of God. God was disturbed by how much they were able to accomplish, how driven they were to succeed, and how capable they were when working as one. He destroyed the tower and scattered man all around the world, separating them into nations, and changed their languages so they could never understand each other enough to put together such a powerful effort ever again. The game reminded me of this the most because that's exactly what Shepard is doing. He's crossing countless age-old barriers in an effort to bring all civilizations together and challenge a force that comparable to God himself.
So, in case it hasn't already become clear, this is my theory on what ultimately drives the reapers: They must remain unchallenged. They cannot allow organic life to become their equals. They cannot allow us to become so advanced that we would be able to venture into their "unfathomable" realm and overthrow or destroy them. As Sovereign says, organic life is an accident. There's no way to prevent it from springing back up again. All they can do is stop it before it becomes uncontrollable. To do so, they come every 50,000 years to wipe us out, at the apex or our glory (according to Sovereign), and force organic life to start all over again.
In addition to this, they do harvest us for other reasons. They use us as slaves (collectors), materials, and resources to build onto their own vast civilization and create more reapers to join their ranks. We are food, fuel, medicine, energy, and a number of other things for them. While they don't need us to survive, they depend on us for growth and rejuvenation. So while they do not want us to advance too rapidly, they leave behind the Mass Relays to help spread the "seeds" of life all over the galaxy and the knowledge stored on the Citadel as a sort of fertilizer to help their "crops" grow. This way, our number is greater and we are much more capable slaves.
The trouble they ran into in this cycle is that 50,000 years wasn't soon enough. We were already advanced enough to not only comprehend them but to come together and devise a way to stop them. Thanks to the addition of humanity, the galactic civilizations were no longer weak, and the Reapers were no longer unmatched - despite what Sovereign and Harbinger both believed.
Now, I know that the Reapers' motives are already set in stone, but considering how simple, hypocritical, and stupid they are, I'd rather believe that Casper is a goddamn liar and it's actually something more along the lines of what I've presented here. In other words, "I reject your reality and substitute my own."