Physical Danger
The amount of danger you're in as a park ranger varies depending on which park you work in and what type of job you're assigned to. If you're a ranger whose job it is to keep the peace at some historical monument like the Lincoln Memorial, chances are you're reasonably safe—barring a terrorist attack or some other extraordinary event.
Even working at one of the many nature-y National Parks isn't guaranteed to put you at risk. For example, park rangers who focus mainly on education programs aren't in all that much danger of physical harm (although some kids do have a mean bite on them).
Rangers whose main job is law enforcement, search and rescue, or fire prevention, however, face a ridiculous amount of danger. How many jobs are there where you might actually have to face an angry bear, or climb a mountain in a thunderstorm, or keep your cool while fighting a blazing inferno? Yeah, that sounds like physical danger to us.
You also have to consider the fact that all rangers in the park might be called in to help with a big emergency no matter what their assignment is. So there's always a chance that danger might come your way.