After the downfall of Voldemort, what happened to the Death Eaters?
They committed many crimes, including mass murder and torture. Nothing in the books made mention of their punishments. What happened?
Imprisoned in Azkaban.
In Pottermore, The Malfoy Family gives a hint about what happened in the aftermath of the war:
So we have the capture (and presumably imprisonment) of high-ranking Death Eaters, but the Malfoys escaped prison for collusion. This was corroborated by a post-Deathly Hallows Bloomsbury web chat:
JK Rowling said in a 2007 interview with NBC that Harry and Ron “utterly revolutionised” the Aurors, and presumably Ministry justice systems. In Draco’s case, I think Harry saw the capacity for remorse, and might have been willing to offer Draco a second chance.
ETA: One thing that’s clear from the top of the astronomy tower is that Draco is being coerced, not acting out of free will. I think the film showed this best (although the book has a very similar passage):
I think this adds to the idea that Harry would want to give Draco a second chance.
I don’t know exactly what form Ministry justice took post-Voldemort. I’m sure Harry would have ensured that execution was off-the-table (in the spirit of Moody and Dumbledore, if nothing else). From the same Bloomsbury chat:
So we can infer that Azkaban was still used as a prison, with more humane measures than before. That would be where most of the Death Eaters ended up.
And from the same chat again, we learn that it wasn’t just fully paid-up Death Eaters who got this treatment:
I would imagine that Harry, Ron and Hermione all pushed hard for this legislation and retribution (and took particular pride when Umbridge was convicted).