According to the olympic website, the US has 3 events it has never won a medal in----I know one of them is Handball, but do not know the other two.
Through the 2006 Winter Games, the U.S. has never won a medal in biathlon and nordic combined.
Through the 2008 Summer Games, the U.S. has never won a medal in handball, Table Tennis, rhythmic gymnastics, and Badminton.
Of the sports in the current (2008) Olympics, USA has never medaled in table tennis, handball, badminton, and triathlons.
Albania, San Marino, Montenegro, Malta, Cyprus, and Bosnia and Herzegovina.
Ghana has never won a winter Olympic medal.
India
Through the 2008 Games, Laos has never won an Olympic medal.
Believe it or not, Brazil has never won Olympic Gold in football (aka soccer).
Nordic combined and Biathlon.
Albania, San Marino, Montenegro, Malta, Cyprus, and Bosnia and Herzegovina.
Albania
It will probably never happen!
Singapore has never hosted the Olympic games
Ghana has never won a winter Olympic medal.
India
Nick never participated in the Olympics
There has never been a United Arab Emirate athlete who won a medal in an Olympic fencing event.
Through the 2008 Games, Laos has never won an Olympic medal.
Biathlon, Cross Country Skiing, Curling, Luge, Nordic Combined, and Ski Jumping.
Never shy in the size of their teams the Australian Olympic team is around 433 athletes which no doubt will be one of the biggest competing.