When I finished my thru-hike of the Appalachian Trail, the question I was most often asked was: "Did you see any bears?" I saw four, and I found out later that some fellow-hikers right behind me spotted two cubs in a tree, that I had missed!
The first bear I saw was in Georgia, and I wasn't even hiking. I had just moved off-trail to a road and was hitching into town to resupply. A lady in her pickup stopped for me, and just as she emerged into traffic, a huge bear lumbered across the road in front of us.
I missed those two cubs in the Smoky Mountains, but In northern Virginia a bear right on the trail bounded away from me just as I spotted him.
The other two bears I saw were in New Jersey, which surprised me. I didn't see any in New England, which is where I expected to see them. At Pochunk Shelter, in New Jersey, I was tented next to another thru-hiker. "Bear!" she yelled. I got concerned as I peeked out from my tent and saw a large bear bounding towards us. She started beating her pole tips on a rock and kept on hollering. At the last minute the animal swerved off into forest.
On my hike, I also saw a moose, lots of deer, a porcupine (fat and unconcerned about me, as he waddled up the trail about ten yards in front of me) and a rattlesnake that looked like a tree root across the trail, until he rattled (that rattling is loud). I heard beaver splashing, but did not see them as their dam came into view.
I'm sure many other creatures scented and saw me. I can only imagine all the ones I missed.