Moose, especially with young present, can be very ill tempered, and you are likely to encounter them along brushy, marshy mountain streams. Be alert, and be ready to retreat and go elsewhere if you encounter one. They have been known to attack cars and ATVs. Mountain lion populations in Montana have increased to where they are numerous in many areas, and lions have sometimes been aggressive. Keep an eye on young children.
Rattlesnakes live in dry, frequently rocky country at lower elevations.
If you are fishing in such places as the Beartrap canyon on the Madison, walk carefully and keep an eye peeled. On hot days, snakes find shelter during the day, and come out in the evening to hunt. Range bulls can be dangerous. Pepper spray might help. Some ranchers are even raising longhorn cattle.