I've seen bats completely miss an open window but always assumed it was because they were young and frightened out of their fuzzy little minds. You were MOST courageous to give it a hand out of the way. Me, I crawl away, practically screaming, into the bathroom and wait until they've settled before I pop out and open a window and/or door for them. Ended up starving one little idiot to death because I couldn't find him to get him out and he could never find the open window.
My great aunt saved a little hummingbird that somehow got his beak stuck in a screen. She gently pushed his beak back out and he flew off. Me, I've caught a couple of small wrens that have got into buildings and knocked themselves silly which make them easy to scoop up and take back outside.
I caught a minnow by hand once as a kid. Mom took me and a neighbor kid riding our bikes and we stopped at a local pond to cool our feet off. A school of minnows came up to feed on whatever was in the cloud of mud we stirred up so I reached down and caught one in my cupped hands to everyone's amazement. But probably others here have hand caught fish before.
I had a bald eagle zip by my second story kitchen window in downtown Marlborough NH. I almost stopped breathing when I realized what it was. Houses in the neighborhood are almost all on little quarter acre lots so it's not where you'd expect to see one. I always guessed it followed the Minnewawa Brook (yeah, that's really its name) looking for fish and followed a cluster of pigeons into the neighborhood to try to take one for a meal.
Eons ago in the late 60's, we saw elephants in a field in Vermont. I was maybe 4 or so and we were travelling to Middlesex to see my sister and her kids. Up what looked to me like the most ginormous hill ever was a big elephant and a smaller one. There's a fuzzy photo Mom took after she made Dad stop the car. No one ever believes us until we pull it out to show them.
Mostly I feel embarrassed by how much cool stuff people on this forum have done. I guess I make wallflowers look like wild floozies in comparison.