We get an extra day!
It's funny how we also have other events that only occur every four years, such as presidential elections and the Olympics, but they don't fall on Leap Day.
You'd think a strange day like Leap Day would play a more prominent role in fiction than it does. Since this is traditionally the day women can propose to men, that would be an angle worth pursuing. Probably the most famous use of Leap Day in fiction is in The Pirates of Penzance. Much less famous is another event from one of my early (and unpublished) works, Day of All Seasons. In that book, the weather in the country of Challen got mixed up once every four years, so all four seasons occurred at once. I decided to change that in the new version I'm writing; now, Chaos Season can happen at any time. It makes things more complicated for my heroines.
Do you think Leap Day is special, or just another day? What would you like to see happen once every four years?