Where did the Reapers come from, they are a species of machine, so how did they come to be? Were they built, or like the transformers, who just "grow"?
"Reaper? A label created by the Protheans to give voice to their destruction. In the end, what they choose to call us is irrelevant. We simply... are."
There is a lot of information about them here -- I'll copy the summary, but the whole page is worth a read (beware of the obvious spoilers of course)
Reapers were created I think about 2 billion years ago or 37 million years ago.
Anyhow, they were created by the Leviathan, an over-confident species that controlled most species through indoctrination, which was a talent they had by birth, as almost all the species that served them were just about slaves. They made note that the species that served them would make "synthetics" to help out.
These "synthetics" however, would usually rise up violently and destroy their creators, causing the Leviathans to lose precious slaves since synthetics couldn't be indoctrinated. So what they did was they made a synthetic solution of their own called the Catalyst.
The Leviathans created the Catalyst to help oversee organic and synthetic relationships. It was given a mandate by Leviathan to preserve organic life at any cost, but this would prove to be their downfall. The Catalyst gathered some pawns (kind of like the Collectors) and went across the galaxy watching relations and secretly gaining genetic material, and after a while it came to the conclusion:
Without warning the Catalyst attacked, slaughtered, and processed its creators into the first Reaper, we call HARBINGER. Some of the Leviathans managed to get away and hide until the final cycle, aka Mass Effect 3. But without any leadership or a guide whatsoever, the thrall species that once belonged to Leviathan became the next victims of the harvest.
This became the first harvest in Reaper history and was also the beginning of the Reaper cycle. The Catalyst decided to speed up the evolution of organic species by building the relays and the Citadel. The Catalyst hid itself in the citadel while Harbinger and the first true Reapers decided to hide in dark spaces. This would be the beginning of the cycle until the ending in Mass Effect 3 depending on your actions in-game.