Many South American countries improved significantly following the rise of democratization and the fall of many of the military regimes of the 60s-80s.. but none are completely free of corruption. Argentina post-1982 is an example.

It's funny to think that not so long ago, parts of the United States were considered horribly corrupt by today's standards. Not too long ago, I read Street Corner Society by William Foote Whyte. Whyte one of the first sociologists to do ethnography in America, and this book was published in 1943 based on research done in the 1930's in Boston. It's usually cited today because it has a lot of interesting insights into how social rankings work in groups, or how culture effects outcome, and how structure plays into culture, or how the slum is ordered through formal and institutions, and things like that. One of the most interesting bits for me, however, is in the appendix he talks about voting day in "Cornerville". The ward bosses organize local boys to be "repeaters", that is, people who vote multiple times in the names of people who had not yet voted. If I recall correctly, Whyte says he only voted two or three times, but some of the other people he knew voted dozens of times. This is on pg. 237-240. See if this link works for you. Among other things, Whyte says, "Widespread repeating is not possible without the co-operation of the election boards." In this local election, Whyte says

There were said to be over fifty repeaters operating with these motorized units, and each man voted twice in each of the twenty-odd precints. This would account for a bloc of over two thousand votes. Branagan's repeating, being much larger in volume, added to his margin of victory, but repeating in itself did not decide this particular election, for Branagan had a clear margin of legitimate votes.

The next section you might also find interesting, as it's about "the nature of political obligations".

This is not isolated. While I don't know if it was ever proven, as late as the 1960 election of President Kennedy, there have been allegations that corrupt voting in the U.S. changed history (the machine in Chicago is supposed to have helped Kennedy win the close race in Illinois, which gave him the electoral college). See this article. Nixon's preliminary investigations found nothing, but they wouldn't have found anything like the "repeaters" that Whyte saw in Boston in the 1930's (the ability to hide the fraud by doing it at the local level without a paper trail across the city was probably not accidental--the conservative Chicago Tribune wrote, "once an election has been stolen in Cook County, it stays stolen.")

Before that, you have obvious corruption, especially in big cities. Just look to Tammany Hall in New York. You can find several similar organization in other American cities (other commonly cited examples are the Chicago political machine, or Huey P. Long's tenure in Louisiana). I think, for the most part, there wasn't one silver bullet that wiped out corruption in America, but lots of little, incremental improvements including not only legal changes but cultural changes (where both voters and the state and federal governments agreed to make it a priority to change municipal corruption--which, by the way, is not at all completely extinguished, though it's normally today only at a very high level, unlike the petty corruption of clerks and police officers you might see in more newly industrialized countries).

What do you mean by relatively modern