Moose: Drove down Emigration Canyon road just a few miles from downtown Salt Lake City at ~3am on a moonless night in the early spring (no snow on the ground, but still cold at night). Coming around a corner I managed to stop about 20 feet in front of a enormous cow standing on her spindle legs in the middle of the two lane road. She stayed in my headlights for about 4 minutes before laconically wandering off to the side.
Cougar: Hiking in the Glacier Peak Wilderness in North Central Washington with two other folks in about mid-June, we came around a bend in the trail that opened into a large rock field - boulders the size of cars. After taking about 8-10 steps into the sunny open area, we heard an odd squeal/squawk. Assuming it was a weird marmot call, we kept walking…for about three more steps when I saw a cougar sprawled across the top of a boulder about 80 feet ahead enjoying the mid-morning sun. A decent breeze was in our face and the sun was behind us - and the animal was a good five feet off the ground…but I still have no idea if it knew we were there and just chose to ignore us or what. As we slowly retreated, we heard (and saw movement) that suggested the cougar had a pair of kittens (or perhaps we imagined that part)
Bear #1: (Also in Washington State - North Cascades). Standing near a power pole at the edge of a small mountain town enjying the view, a black bear cub came charging out of the undergrowth, jumped on the pole, and climbed about 4-5 feet off the ground - I was less than twenty feet away. It finally noticed me about 20 seconds later, made a surprised little “woof!”, jumped off the pole, and ran off into the brush. I had a cheap disposable camera in-hand and got a couple of quick shots off - without those I would have thought I dreamed the whole thing up.
Bear #2: While trail running on a Forest Service logging road (North Cascases again), I was in the zone and not paying enough attention. I ran around a turn…and right between a sow feeding on one side of the road and her two cubs just a few feet in the short brush on the other. The sow alerted me to my dumbass mistake with a loud bark about 20 feet to my left - scared the living piss out of me, but my legs had a mind of their own and just kept going down the gravel/dirt road without breaking stride (though my head swiveled left-to-right so fast I have no idea how I kept my feet). When I finally pulled-up I was about 300 yards down the road on a straightaway. About two minutes later I heard the cubs start arguing about something, the sow cross the road to break it up, and they moved away noisely down the hill (and, thankfully, away from me).
I spent the next twenty minutes sitting on the side of the road twitching and trembling - an encounter that could have ended much less well.
Random encounters: Many, many close encounters (some unlucky, some stupid) with snakes - venomous &/or constrictors) on several continents. Had a water buffalo step on my tent (and almost my head) in a beach wind storm. Various nasty jellyfish interactions while diving. Some big cat with a throaty cough did laps around my “cabin” in Panama one night (local folks said it was a jaguar, but a cougar seemed more likely) for what felt like an eternity.
(Re-reading the above, I’m surprised I’ve made it this far without, um, being food. Urk.)