Some claim that New Hampshire's Grand Monadnock is the most-climbed mountain in the US—and second or third in the world, behind China's Tai Shan and Japan's Fuji.
Depending on how you define a climb, Monadnock is not even the state champion. Every year, more than a quarter million people "climb" New Hampshire's Mount Washington via car, cog railway, or on foot. By comparison, Monadnock State Park has only 120,000 visitors per year, and we can assume many of those don't make the daunting hike (4.2 miles climbing 1,800 feet) to the summit.
Tennessee's Clingmans Dome averages 600,000 visitors per year, according to the Great Smoky Mountains National Park. North Carolina's Mount Mitchell State Park counted 398,000 in 2016. Both of those summits are easily accessible by paved paths from the parking lots. Colorado's Pikes Peak had 340,000 visitors in 2014, including 15,000 hikers. New Mexico's Sandia Crest estimates a half-million drive-ups each year, plus another 200,000 who ride the spectacular Sandia Peak Tramway.
For what it's worth, Le Conte Lodge has about 12,000 overnight guests each year. But that is no limitation on the parade of day hikers. For example, Ed Wright climbed Le Conte 1,310 times, and as far as I can tell, he never stayed overnight at the lodge.
One way that Monadnock can match Le Conte is in the zeal of some of its climbers. Larry Davis hiked up Monadnock for 2,850 consecutive days in the 1990s and made his 7,450th climb on January 6, 2017. Another climber named Garry Harrington told me he has summitted Monadnock about 1,100 times.
On California's Mount Baldy, Richard Tufts has logged more than 1,000 climbs, and 78-year-old Seuk Doo Kim is aiming for his 1,000th in 2017.
Other than Davis, I have found no one in the nation who has climbed one mountain more times than Le Conte's all-time leaders, Ron Valentine and Jack Huff. According to Multiple Repeats by a Member on the peakbagging site listsofjohn.com, the national leader is Rick Baugher, who made his 1,000th climb of Kelly Mountain, Idaho, on January 11, 2016.