Every year National Park Service publishes the Annual Park Ranking Report for Recreation Visitors.
More than 330 million people visited our national parks in 2016 (src: nps.gov stats)
You can see the complete list at http://nationalparksimages.org/parksrank.html
Here are the ones that made to the top of the list. Let us know (in comments) how many of these you have been to.

#1. Great Smoky Mountains National Park, North Carolina/Tennessee (11,312,786 visitors)

Grand Canyon National Park, Arizona (5,969,811 visitors)

Yosemite National Park, California (5,028,868 visitors)

Rocky Mountains National Park, Colorado (4,517,585 visitors)

Zion National Park, Utah (4,295,127 visitors)

Yellowstone National Park, Idaho/Montana/Wyoming (4,257,177 visitors)

Olympic National Park, Washington (3,390,221 visitors)

Acadia National Park, Maine (3,303,393 visitors)

Grand Teton National Park, Wyoming (3,270,076 visitors)

NationalParksImages.org
See the complete list at http://nationalparksimages.org/parksrank.html