Avoiding the woods for fear of the creatures that may be lurking there certainly sounds like a good idea when you read news stories about animal attacks. In reality, though, you can avoid animal attacks by following very simple rules. Learn more below.

Bears
Black bears want your food. They're also smart and we're also bad at keeping them from it, so in many frequently-visited outdoors hotspots, they've learned to think of us as a food source.
That's silly, because keeping bears out of your food is pretty easy. Buy a bear canister, put all your food and food-scented stuff in it at night. Put that canister 100 yards outside your camp at night. Et voila: the bears will leave you alone.
Brown bears want to be left alone. Take pains not to surprise one while in brown bear territory and carry bear spray to dissuade them from attacking you if you do accidentally stumble across one.
Never, ever get between a she-bear and her cubs.
Wolves
We've nearly hunted wolves into extinction, so they're scared shitless of us. They'll hear you coming from miles away and give you a wide berth. So, if you do see one, it's likely because you're hiding in a hunting blind or moving rapidly in a vehicle and the animal is not a threat to you in either situation. Wolves only represent a threat to injured, sick or otherwise weak humans. You do have to worry about your kids a bit, just common sense stuff you'd do anyway like not letting them wander off into the woods alone at dusk.
There's an awful lot of misinformation and fear mongering around wolves; the subject has simply been politicized by their reintroduction in some western states. Realize that what you're hearing is exaggerated and politically motivated and ignore it. Wolves are exceptionally rare, count yourself lucky if you ever get to see one.
Coyotes
Now you will see coyotes. We've got little ones out West and you've got big ones that have bred with wolves back East now. Neither is particularly scared of humans and, while they do represent some common sense threat to small children, what you should mostly worry about is Poochie the Pomeranian. In packs, coyotes can be a threat even to large dogs and they actively hunt their domesticated cousins as a food source. Coyotes can clear fences, so the only solution is to keep your pets inside unless supervised.
Snakes
Have your dog trained in snake aversion. There, a professional handler will fit your dog with a shock collar, then walk him around a course of caged snakes. Every time your dog shows interest, the trainer will zap him. They learn to not be interested in snakes in no time. Carry Benadryl when you're outdoors and give it your dog immediately if he is bit, then get him to a vet.
For you, just develop an awareness of likely places snakes hang out, then don't go sticking a hand or foot in those places. Bushes, holes, log piles, under rocks and pieces of lumber. Snakes just want to be left alone.
Sharks
Sharks are only interested in humans if a) they mistake us for food or b) we draw their attention by fishing or bleeding. If you're in the water with dead fish, keep those dead fish away from you, such as on a stringer attached to a float. If a shark wants your fish, let him have them.
Alligators
The best way to avoid alligators is to avoid bodies of water where they live. It's that simple: stay out and stay away from the banks, too. We all saw Crocodile Dundee.
Mountain Lions
If you see one or suspect one may be stalking you (they're sneaky!), act like the big, scary predator that you are. Hold yourself upright, grab a stick and look the lion in the eyes. Shout at it and wave your arms. Slowly move away, but never turn your back to a lion and don't run; doing so triggers their prey drive.
Mountain lions are easily capable of overpowering and killing a grown man, but no one's told them that and, like all other predators, they remain terrified of human beings. Predators are naturally scared animals because their existence hangs on a thread; if they lose the ability to hunt at their full physical fitness through even a minor injury then they're done. And they know it. If you're scary enough, they'll leave you alone.
The One Rule For Successfully Avoiding Animal Conflict
Store your food and waste properly, keep an eye on your kids and put your dogs on a leash and there's absolutely no need to ever have a negative experience with wildlife. Just leave the animals alone and they will leave you alone. Be respectful, not scared and enjoy your opportunity to observe a rare slice of nature.

Keeping your food under wraps and letting the animals know who's boss by making noise and not running are the most effective ways to avoid conflict with these creatures.

In most cases, predators attack as a result of extreme stress or simply because you got between them and something they wanted.

All that said, though, it is still an excellent idea to keep your children supervised at all times when entering bear or wolf country; they are small enough to be mistaken as prey and very few predators will bother to attack if the children are supervised.

For more information regarding predators and how to avoid conflict, check out the original article at Gizmodo.