I always think Denver is such an odd one on the top 20 list... is it United's biggest hub? I don't remember seeing that is has huge numbers of Lon haul flights? Is it just that big due to domestic?
DEN is like ATL, only smaller and more domestic in focus. It was modeled after ATL and is a very modern airfield and facility, making it a very efficient place for an airline to do business. It makes connections pretty easy, but Denver is also large enough and growing enough as a city to hold its own weight. 65% of passengers are O&D, so it's not strictly a connection airport by any means. It's well-situated to pull from all corners of the country as it's not much more than two hours at most to the west coast and four hours to the east coast. The isolation of a lot of places in the mountain west make flying a more competitive proposition over driving, unlike many other regions of the U.S. The airport has been fully paid off, so landing fees are low again. It's no longer a fortress hub, so the competition is very healthy. The two largest tenants, UA and WN, both have plans to grow traffic there. It was UA's #2 hub pre-merger, but it's been a solid #4 now behind ORD, IAH, and EWR. There is more international service at DEN now than ever, with a handful of flights to Europe, a decent number to Central America, and the daily NRT. It's not a huge number of international flights, but that's more than any of DEN's regional peers can claim.
For most years in the 2000s, DEN was the fifth busiest in the U.S. and in the top ten worldwide, coming just behind FRA. DEN hasn't dropped off by any means — passenger numbers are still growing — but lots of other airports like PEK, PVG, JFK, AMS, HKG, IST, and CAN have outpaced DEN's growth. It's also important to remember that DEN, ATL, et al only have one airport for the entire metro area. If NYC, LA, the Bay Area, and Chicago all had centralized airports with no capacity or operational issues like DEN, they would all shoot to the top of the list.
My guess is that had the city of Denver never built DIA and instead tried to make what they could have with the landlocked, inefficient, and overflowing Stapleton, DEN probably wouldn't be in the top 30 worldwide.