This infographic from TitleMax.com shows the number of visitors for 15 national parks, starting from 1980 through 2015. Worth noticing that top 5 most popular parks kept their position almost entirely over the past 35 years, with a rare exception.
This information and some additional research might be useful if you want to avoid the crowd, and find a more quiet location.
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Irma Wallace
Co-founder and Vice President of SearchRank, responsible for many of the day to day operations of the company. She is also founder of The Arizona Builders' Zone, a construction / home improvement portal.