This question tends to come up quite often and, depending on who you ask, you are likely to get a number of answers--everything from no never to yes always to yes or no depending on the situation.
Although I have friends who range from those who don't own a firearm, don't want to own a firearm, and would never carry a firearm anywhere to people who are never more than a foot or less away from their firearms AT ALL TIMES, I'm one of those yes or no depending on the situation people. In almost all cases, the reason I carry a concealed weapon is for threats from two legged animals, not the four legged variety.
When I am in the woods, I am of two minds when it comes to carrying a firearm. If I will be camping I always bring a firearm with me as there is more of a threat from people coming up to a remote spot in their vehicle. Also, driving to a spot in the woods allows for me to carry my firearm of choice and ammo (no weight restriction), and there is often a spot or two I can hop out and do a bit of shooting along the way.
On the other hand, when I am hiking or backpacking, I never feel the need to take a firearm with me. First, the added weight is more of a liability than an asset, and second, I figure that someone who is hunting a person for whatever nefarious purpose (to commit a robbery, etc) isn't going to haul themselves ten miles down a trail to do so (and then have to schlep their ill gotten gains back out on foot).
But what about wild animal attacks? Having never been the victim of such an attack (knocking on wood), I can say that I use a number of other measures in an attempt to prevent such an event. I have my trekking poles, a fixed blade knife, and bear spray. I keep a clean camp and try not to smell like fried bacon as I hike down the trail. I make plenty of noise (apparently my singing could route a bear at a hundred yards...or so I've been told), and I try to make myself as aware of my surroundings as possible.
Yes, people have been attacked by wildlife and yes, I'm guessing in that moment anyone in their right mind would feel better with a firearm in their hands, but logically, it doesn't make a whole lot of sense to carry a firearm in the minuscule chance that you will need it. Add to that the minuscule chance that the firearm you are carrying will take care of the threat (a black bear will probably laugh at your choice of firearm since the tiny .380 that fits in your pocket won't get the job done and if a cat wants a swipe at you, you won't even hear it coming until the swipe has been taken...then try to draw...).
As with everything firearms related, it is a personal preference where you need to weight the pros and cons of your decision to carry or not carry.