It depends on the country, but the vast majority of countries play either football ( soccer) or baseball as their primary sport. For example, in Nicaragua, football is the number one sport, but in Panama the number one sport is baseball.
If you mean America as in North and South America, then the sport would be soccer. If you mean America as in North America, then the sport would still be soccer. If you mean America as in the United States of America, then football (American Football) would be the answer.
A bullfight is not 'played' as one would play a sport. A bullfight is performed in an arena called a plaza de toros (bullring). Fights are held in Spain, Mexico, Portugal, France and a number of countries in South and Central America.