Attacks on humans by cougars (also known as mountain lions and pumas) are becoming more frequent, and especially more publicized in the past few years. In the small town in Oregon where I live, cougar sightings and reports of cougars carrying off small pets and farm animals are very common. Some of this is due to a genuine increase in cougar population, and some of it is political...a response to the outlawing of hunting cougars with dogs a few years ago.
The truth is that cougars are becoming more plentiful in many parts of North America and they are becoming more acclimated to human presence in their territory. Attacks are still very rare, and fatal attacks are even rarer. I researched this pretty completely, and found reference to only 4 fatalities in the past ten years. It is still important, though to know what to do in case you ever come across a cougar in the wild.
Cougars look for easy prey. That means small, defenseless prey that is alone. Children and pets should be kept close to the group when hiking in cougar country. Hiking in groups helps in preventing cougar attacks. If you are confronted with a cougar, pay attention to his body language. If the cougar is looking away and moving away from you, stay still and don't move. Always try to look as big as you possibly can, by raising your hands over your head, by holding up sticks, by standing up straight. NEVER bend down or run. Cougars hunt running things, and turning and running triggers hunting instincts in the animals. At least two of the recent fatalities were runners moving through cougar territory. If the cougar is displaying stalking behavior, that is crouching or staring intently, stand firm, look big, maintain eye contact, yell, and bare your teeth. If you ever are attacked, fight back with everything you have. NEVER play dead. This does not work with cougars. Fight back, and you have a fairly good chance of surviving.