I'm excluding Alaska, both because it's just different, and because I've only visited once and thus have insufficient knowledge. That being said..
The best/most important/greatest national park in the lower 49 is, bar none, Yellowstone. I've been to most of the rest, am very familiar with some of the other leading contendors, and quite frankly nothing else comes close. Some reasons in order of importance.
1: Full spectrum of native mammals, most importantly bison, grizzlies, and wolves. National parks exist to remind us that the world is bigger, greater, and much more important than humanity. Nothing comes close to reinforcing that, in an immediate and emphatic way, than multiple critters that can kill you if you act dumb or just have bad luck.
2: It's big! Size matters, being able to get far from the road in the second biggest reinforcer of human smallness. While it can be argued that other parks provide more effective isolation (ie a shorter distance from roads, but longer travel time due to trying conditions), the answer to that is contained in my third point.
3: A burly winter. More humans live near the tropics for a reason. Cold and snow change a landscape completely, and winter in Yellowstone is 7-8 months long. Yellowstones geography not only make it colder than the surrounding areas, but increase its snowfall exponentially. The result is that Yellowstone is two parks; the friendly tourist mecca of June-September, and the potentially harsh snow-bound land of October-May. Even though snow machines and snow coaches run almost all winter, and even though the park service could plow the road to Old Faithful if it wasn't such a cash cow, winter increases Yellowstones size many-fold.
4: A unique and varied landscape. All that snow melts, which creates the animal haven that is Yellowstone in summer. Elk and Antelope migrate hundreds of miles because doing so is the most calorically efficient thing in the long run. The snow also allows rugged mountains, rolling hills, huge meadows, and rivers large and small to coexist in close proximity. Snowmelt creates the largest high altitude lake in North America, and the largest concentration of thermal features on the planet. Cut Yellowstone into four equal pieces along the cardinal directions and each of the pieces would still be a national park of greater stature than all but a handful of the rest.
Perhaps the greatest national park is the one that almost existed in the 30s, but almost certainly will never come to pass in my lifetime (if ever). Colorado Plateau National Park. Imagine Arches expanding south into the La Sals, linking into Canyonlands, spreading south over the Bears Ears to connect with Natural Bridges, sweeping over Dark Canyon and the Robbers Roost, the southern San Rafael Swell and enveloping Capitol Reef, the Escalante, the Aquarius, Bryce, the Markagunt, and ending in Zion. Ideally, it would encompass the Kaiparowitts and Kaibab, and the Grand Canyon. Almost everything, in short, north of Arizona, west of Colorado, south of I-70, and east of I-15. Imagine Lake Foul never coming to be. Imagine that, in the 30s, not a SINGLE PAVED ROAD existed in this entire stretch. There's a reason so many people get obsessed with that vulvic landscape.