The U.S. does not have a huge bio-diversity of animals. Its important to hold onto the species we have. Cats in the USA are pretty rare. Other than the zoo, I've never seen a bobcat, or puma, or cougar.
I've never seen a Cougar in the wild either. Yet they are rather abundant here in Colorado. Some places, like Boulder have serious problems with Cougars attacking dogs right in peoples yards. We have a hunting season on them here to control their numbers.
As several others have stated, you will NOT see a Cougar under normal circumstances unless it wants to be seen or has no fear of humans. These animals are normally very secretive and are quite capable of evading humans long before you have a chance to see them. Thats why Cougars are normally hunted with dogs.
Predators will normally kill whatever is easiest for them to catch. The less energy they expend making a kill the better it is for the animal, especially during winter months.