The Impeachment and Trial of John F. Kennedy is by far the most intriguing alternate history concept I've ever heard.
1. Suppose JFK survived the assassination attempt unharmed.
2. The investigation would have been, perhaps, more intense.
3. As a result, a lot of the potentially scandalous stuff about JFK's life become public knowledge all at once, rather than the trips and drabs we've gotten in real life.
4. And some of that stuff was potentially impeachable offenses...
It's by Harry Turtledove and Bryce Zabel, and a good chunk of it is online at the linked site.