18 Days

The first sentence on the wikipedia entry for "Curse of LaBonte" describes it as "quite possibly one of the most famous curses in curling history." From what I can understand, (and I am the first to tell you I cannot for the life of me understand the rules of curling,) at the 1972 Curling World Championships, after the U.S. competed against the undefeated Canadians, it was unclear as to who had won. An American on the team, Bob LaBonte, thought the U.S. had won and jumped in the air to celebrate. As he landed, he accidentally knocked into a Canadian stone, moving it ahead of the Americans' stone, thus awarding the win to Canada. It took 8 years for Canada to win another World Championships, which sparked comments that LaBonte had put a curse on them.

The 2010 Winter Olympics come 18 months after the previous Olympics, the 2008 Summer games in Beijing. (This same time period applies between most summer and winter Olympics.)

Larrisa Latynina, a gymnast from the former Soviet Union, finished her Summer Olympic Games career with 18 total medals, the most in history.

18 Mormon athletes participated in the Sydney 2000 Summer Olympics, and they won one gold medal and one silver medal. That's 10 athletes and one gold medal more than that at the Salt Lake City Games, in 2002, a city founded by Mormon pioneers and currently headquarters to the Mormon church.