I love Bryce, Zion, Yellowstone, Grand Tetons, Rocky Mountain, Carlsbad Caverns, Arches, Banff, Buffalo River, and Big Bend. I really like the North Rim and South Rim of the Grand Canyon, Pacific Rim, Yoho, Jasper, Guadaloupe Mountains, Mesa Verde, Mount Revelstoke, Canyonlands, Dinosaur, Petrified Forest, Capital Reef, and the Great Smoky Mountains. I was pretty non-plussed with Mammoth Cave and I didn't care for Hot Springs.
Here are a few pictures from some of my more recent visits:
Elk crossing Sprague Lake in Rocky Mountain National Park
Our family canoe on the Buffalo River
Bears at Pacific Rim
Alpine Meadow at Mount Revelstoke
Two Jacks Peak at Banff
Grand Tetons
Grand Canyon of the Yellowstone
And of course, the best way to get to know a National Park is to camp there.