I remember my mum taking me for a walk in the woods when I was little, maybe 7 or so. We came across an owl, probably a barn or snowy not sure now. We were literally a few feet from its perch low in the branches - it was in the branches not us..
It just sat there watching us for a while before flying off.
A few years later while fishing off the pier in Dunoon, I found a line that had been hung up by some stairs leading down to the water and left there. I started to pull it in, and it was a long line 100m or so, eventually I pulled up a wee cod, perhaps a couple of pound. Next thing I heard was a snort - looking down I saw a grey seal looking up at me, it had obviously saw this fish flying through the water and was chasing it. Luckily for us both it never got it, I shudder at the suffering it would have gone through if it had caught the cod with the hook and all.
A couple of camping trips ago, saw a pair of eagles and an eaglet, they were training it, one flying off and calling, the other then doing the same. Saw several deer that had been sleeping in hollows or track side ditches till we wandered past only to see them jump up and run in front of us.
Perhaps the most surreal was chatting to a couple of friends at his front gate, a small tree beside us in the garden with a blackbird in it. I did a sort of light bird whistle and it jumped up and flew straight at me, staring straight at me - eye to eye like before veering off a foot away from me... no idea what I said to it..