What Counts as an Olympic Sport?

It depends on the year.

In 1896, freestyle swimming for sailors was on the lineup. In 1920, tug-of-war. Live pigeon shooting was a new event in 1900 (like 184 other events through the years, it lasted for only one Olympiad).

For a look at how long each Olympic category has been around, take a look at a fascinating infographic from Wired magazine here.