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)
The Reapers, known by the geth as the Old Machines, are a highly advanced machine race of synthetic/organic starships.
The Reapers reside in dark space, the vast, mostly starless space between galaxies. They hibernate there, dormant for thousands of years, before they are given the signal to return.
Their origins are completely unknown. The first Reaper known to have communicated with organic life, referred to by Saren Arterius as Sovereign, claimed that the Reapers have neither beginning nor end.
Even their true name is a mystery; "Reapers" was a name bestowed by the Protheans, and Sovereign stated that whatever the Protheans chose to call them is irrelevant: "we simply... are."
Sovereign also reveals that the Reapers were the original creators of the Citadel and the mass relay network. These massive constructs exist so that any intelligent life in the galaxy would eventually discover them and base their technology upon them – all part of a scheme to harvest the galaxy’s sentient life in a repeating cycle of purges that has continued relentlessly over countless millennia.
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:
PEACE WILL NEVER HAPPEN BETWEEN ORGANICS AND SYNTHETICS
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.