As a hardcore battleship nut, I simply couldn't resist the idea that the world's biggest battleship, Yamato, had not been sent on its suicide mission.
For those who don't know, Operation Ten-Go was a mission to try and help the defenders on Okinawa as the Americans came to invade it. Most of the Imperial Japanese Navy was staunchly against it, figuring that the remaining strength of the Navy, which had been smashed to bits after Leyte Gulf, shouldn't be sacrificed in a useless attempt to stop Allied advances. The Japanese leadership expected the Navy to try and assist the defenders on Okinawa, but knew full well the ships would probably not (and didn't) make it to Okinawa.
The US had over a dozen carrier launch airstrikes on this group, and assembled a battleship force to take it on if the airstrikes failed. They didn't, and Yamato sank 125 miles from the home islands.
Now, what if the Japanese commanders got their way, and Yamato didn't get sent on its suicide mission?
Now, part of me figures it would face the same fate as Nagato, being used in a nuclear bomb test. But another part of me figures that the Japanese would want to keep it as a museum ship, as they did with Mikasa.