I’ve read that an Axis victory in WWII and Confederate victory in the Civil War are the two most popular departure points for alternate-history writers. What might be the 3rd-most popular? (And others too)
Soviets win the Cold War?
Nationalist victory in Chinese Civil War?
Some alternate candidate wins the US presidency?
Dinosaurs never go extinct? (per the Pixar movie)
Not a Cold War but a hot war–nuclear annihilation where everyone loses.
I would vote for this alternate history if it included interesting but coherent twists.
The Two Georgesscenario - the American revolution never happened, or was suppressed, or peace negotiated. America remains part of the British Empire.
Steam punk, where mechanical steam powered systems became more advanced and other technologies didn’t.
Rome never falling is a common one. Beyond that it starts to get more granular. There are stories for almost anything. I remember there used to be a web site that was just a giant timeline of history and it would mark the point of divergence for hundreds of different alternate history stories.
I was going to suggest that one popular locale in Time Travel (although not necessarily a Point of Divergence) was The Crucifiction, which that list appears to substantiate. In fact, since they’re on the list, they must be divergences Sixteen entries for 30 CE plus or minus 5 years. (And they doesn’t inlude visitors, as with Silverburg’s Up the Line or Michael Moorcock’s story and novel Ecce Home or some others I’ve read.)
I’m not sure that nuclear war is a popular alternate history topic: While there are a great many stories set after such a war, the war is usually set in the author’s future, and often in a deliberately-vague time that could be the future relative to any reader.
Behold the residence!!
Sorry, couldn’t resist 
I was going to translate it as “I can see my house from here!”
Deleted
Centurion: “Right. Now write Ecce Homo one hundred times on the walls, or I’ll cut your balls off!”
I would say the genre where people of this time (or the near future) go back in time and change history. It can be a relatively short period for specific results, such as (Guns of the South, where an arms dealer tries to sell Robert E. Lee AK-47’s or a short story where a jet pilot ends up in WWI, or A Gun for Dinosaur, where the ‘butterfly’ effect is very real.
It can also be a larger number of people in a very different world (Destroyermen series) or changing a world that is already well-known (Ring of Fire, where a West Virginia town ends up in 17th Century Europe).
Not as specific as WWII or the Civil War, but people going back to change history is a common theme. (one more, The Return of William Proxmire by Larry Niven that shows changes aren’t always as they seem…)
OK, press on.