How many different sports are currently played in the Summer Olympics?
Olympic sports
A sport or discipline may be included in the Olympic program if the IOC determines that it is widely practiced around the world, that is, the number of countries and continents that regularly compete in a given sport is the indicator of the sport's prevalence. The requirements for winter sports are considerably lower than for summer sports since many fewer nations compete in winter sports. The IOC also has lower requirements for inclusion of sports and disciplines for women for the same reason. 
Women are still barred from several disciplines; but on the other hand, there are women-only disciplines, such as rhythmic gymnastics and synchronized swimming.