O'Hare airport in the Chicago area. I was once told that on average, there is a plane touching down or taking off every 30 seconds at O'Hare (this was some years ago).
Atlanta is still the busiest airport in the U.S.
Hartsfield-Jackson Atlanta International Airport - Atlanta, GA
London Gatwick
Paris Charles de Gaulle Airport
Hartsfield-Jackson Airport in Atlanta is the busiest, followed by Chicago O'Hare.
SFO - San Fransisco International Airport
Beijing Capital International Airport PEK/BJS is the worlds second busiest airport for commercial traffic.
The main airport in Maui is Kahului Airport. This airport is the second busiest airport in the entire State of Hawaii.
Hartsfield-Jackson Atlanta International Airport, United States of America.
Hartsfield Jackson International Airport is the largest (busiest) airport in North America. It is located in Atlanta, Georgia.
Sao Paulo Brazil is the busiest airport in South America. There is further information at the related link.
London Heathrow Airport, which witnessed a whopping 48.2 million passengers from January to August 2013, continues to be the busiest airport in the UK, with Gatwick a distant second and Newcastle Airport just beating Liverpool John Lennon Airport to tenth place.
Washington Dulles International is the busiest airport in Washington DC
Heathrow Airport.