I answered a similar question some months ago. China has the greatest number of executions. Nobody knows how many but they number in the thousands. The US comes in about fourth (possibly fifth) on the list.

I don't recall who has the highest number of prisoners although I suspect that China again leads the field, … Read more

Which country executes the most would be hard to say, for sure ... Since many countries ruled by tyrants or corrupt governments execute thousands of people a year - but most of them are listed as "missing" since the government doesn't actually admit to killing them.