At least with bears all you have to do is make a bit of noise, they'll hear you coming and bugger off since they don't want to deal with you. And while I would be cautious if there are cougar sightings in the area so long as you hike with a couple people (and you shouldn't be hiking alone in wilds in the first place!) the group should be enough to deter them. So long as you aren't stupid and try to take a selfie with a grizzly you'll be fine.
Spiders just have too many legs and move in a way that freaks me the fuck out. They're important to the ecosystem and all that, I just don't want to be anywhere near them if I can help it.