History
While many wildlife species were protected in the early days of national park management (beginning in the 1870s), predators like pumas, bears, and coyotes were initially considered undesirable and actively hunted. In a striking sign of evolving management and perspective, Yellowstone National Park (the world's first) reintroduced gray wolves in 1995 and 1996, which had been eliminated intentionally by the early 20th century, and they quickly reoccupied their ecological niche.
Hunting and Trapping
Today, hunting and trapping are not allowed in national parks, except under special circumstances.
Harassment
While visitors are encouraged to observe and enjoy wildlife, national parks strictly prohibit the harassment of animals. Beyond the obvious, this also includes simply approaching a creature directly, which can stress it out and promote aggression.
Safety
Such regulations protect people, too: Yellowstone forbids getting within 100 yards of grizzly and black bears, for example, which typically avoid people but can respond aggressively if provoked.
Learning More
Any given park may have its own special regulations concerning wildlife. Check in at park offices and visitor centers to get the full skinny---and to find out the best places to observe animals.