I, personally, think that the only way to see Yellowstone is on the back of a snowmobile.
I've driven through the park in a car a couple of times, and it sucked. And I've ridden through the park on the back of a motorcycle and, while better than a car, it was still way too crowded for my liking. Part of that is because those times were during the spring and summer months when the National Park is the busiest. But it's also because it's just not as much fun as it is during the winter on the back of a snowmobile.
It's less chaotic, less crowded, and wildly different of an experience, something that sticks with you well past when you leave the wilderness it inhabits. Maybe it's the scenery draped in snow. Or the animals moving around in very different mannerisms compared to the summer. Whatever the case, it's just plain cool.
There is, however, a problem. And it's a problem that the entire world faces: people.