As far as popularity, it would be figure skating, alpine skiing, and Ice Hockey.
Summer Olympic Sports- Beach Volleyball, Track and Field, and different swimming events. Winter Olympic Sports- Hockey, Figure Skating, and Bobsledding
Bobsled, Luge, and Skeleton
there are three hockey is in the Winter and basketball and soccer/football are in the Summer
triathalon
Triathalon.
basketball, hockey and snowboarding
sleding skiing and skateing
From the IOC:The IOC establishes the programme of the Olympic Games, which only includes Olympic Sports. 1 Olympic Sports included in the Programme of the Olympic Games 1.1 To be included in the programme of the Olympic Games, an Olympic sport must conform to the following criteria: 1.1.1 only sports widely practised by men in at least seventy-five countries and on four continents, and by women in at least forty countries and on three continents, may be included in the programme of the Games of the Olympiad; 1.1.2 only sports widely practised in at least twenty-five countries and on three continents may be included in the programme of the Olympic Winter Games.
No country has ever hosted the Winter Olympics three times in a row.
Speed skating (long track and short track), ice hockey, and figure skating.
The three Olympic sports that debuted at the 2000 summer Olympics were the triathlon, trampoline, and taekwondo. The trampoline involves doing aerial tricks while on a trampoline.
All but three.