We can't be worrying about wildlife if we want to visit nature, as they are part of nature. I usually carry a bottle of bear spray with me on hikes, just in case, especially if we go to places with lots of bear sightings. But most of the trails we go to are by the coast with black bears being the common species; and black bears are usually not aggressive, usually only mind their own business, and won't approach humans even if you run into one. Mountain lion sightings are even more rare, as they usually avoid humans. Staying on trail and continue to make sound / noise during hikes is a good way to let wildlife know that you're approaching and they usually avoid you.

After being on so many hikes, I've only ran into a black bear once on Mount Seymour. #438583 It was during fall, and the bear was chowing down on berries, fattening up to prepare for hibernation.