Ahead of their final report due in April, Airports Council International has released their preliminary passenger data for 2016. Based upon passenger count, the world's busiest passenger airport is Atlanta's Hartsfield-Jackson International, with 104 million passengers last year. Second place goes to Beijing Capital International, which hosted 94 million passengers. Coming in third is Dubai International with 83 million passengers. Close behind Dubai is LAX, which saw 81 million passengers in 2016. According to the CNN article that I'm referencing, that was an 8-percent jump from 2015, when LAX was seventh in the world. The Atlanta Journal Constitution also has an article, as does Business Traveller. Check out this Wikipedia page to see airports ranked by passenger count annually since 2002.
So if you're counting passengers, we're number in the world. What if you're counting airplanes? The CNN article doesn't mention traffic count, so I went to the FAA's Airport Operations reporting system. Based on the FAA's data, the busiest airport in the country is again Atlanta, which had 898,356 operations (takeoffs and landings) last year. Up next is Chicago O' Hare, with 867,635 operations. Coming a distant third is LAX, which had 696,890 operations last year.
If you count freight, LAX doesn't rank nearly as highly; in 2015 we were number twelve, with 1.9 million metric tonnes. According to the chart I found on this Wikipedia page, that puts LAX behind Miami, Florida. The busiest cargo airport in 2015? That was Hong Kong!