The USA has never won any medals in Badminton, Table Tennis, women's volleyball or handball. It has never won gold in men's or women's hockey, men's football, judo or modern pentathlon.
Karate is not an Olympic sport. However, Tai Kwon Do is an Olympic sport and there have been a number of gold medals for the United States in this sport.
Since baseball became an Olympic sport in the 1992 Olympics, Cuba has won three gold medals and the United States has won one.
WESTLING IS NOT AND NEVER WILL BE A SPORT. There is a World Cup for Greco-roman wrestling held each year. The 2007 World Cup was held in Turkey in February. Ukraine won 4 of the 8 gold medals, Iran won 2, and the US and Turkey won 1 each.
Baseball became an official sport of the Summer Olympics in 1992. The US has won 3 medals, 1-Gold in 2000 and 2-Bronze in 1996 & 2008.
Since 1980, when women's field hockey became part of the Olympic Games, the United States has never won a gold medal in the sport. In fact, the USA women's field hockey team has only medaled once: in the 1984 games they took bronze in Los Angeles.
Gabby Douglas from the US won the gold for the All-around, Sandra Izbasa from Romania won the vault gold medal, Aliya Mustafina from Russia won the gold for the uneven bars, Deng Linlin from China won the gold for the balance beam, Ali Raisman from the US won the gold for the floor.
The US won 9 gold medals in the 2010 Winter Olympics.
The US won 10 gold medals at the 2002 Winter Olympics.
No, the US has never won the Rugby World Cup.
The United States has never won a dressage gold medal in the Olympics. In team dressage, the US has won 1 silver (1948) and 6 bronze (1932, 1976, 1992, 1996, 2000, 2004). In individual dressage, the US has won 1 bronze (Hiram Tuttle in 1932).
NZ has won 3 or 2 gold medals
The US men's 4x400 meter relay team has won gold in 16 Olympic Games. Great Britain has won the gold twice and Jamaica, Kenya, and Soviet Union has won once.