On steel, if I can see it, I'll take a shot at it. My local range has ~14" steel plates every hundred yards from 300-800, plus one at 940 yards.
I have hit out to 500 with Iron sights on old military rifles, and all of them with glass.
Generally not the first shot, but once I get the drop figured out, I hit about 50% on a good day (meaning lowish wind).
Also shot some ridiculous ranges at Prairie dogs, because you can't really wound them, if you hit at all it is fatal. You either miss or you kill them. Farthest was about 850 yards, based on the ~6 mil of drop. It was farther than my buddies 800 yard range finder could range.
The nice thing about shooting at P dogs that far away, is they generally let you take a few shots about them before they go down.
Took me three shots to hit him, I guessed low on the range and my first shot fell short (you have about 5 inches of drop per 10 yards way out there). I corrected my hold, and the 2nd shot hit a hair low and one dog-width down wind. Kicked dirt on him, and he ran to his hole, but didn't go in. Third shot dumped him.
This was with a custom 6.5-06, 6.5-20X scope, 140gr AMAX, prone with a bipod and my buddy spotting.
As far as long range varmint shooting, 850 is not that big of a deal for the really serious guys. Google: VHA "1000 yard club" There are also 1500 and 2000 yard clubs.
For a game animal, I don't think I would shoot any farther than about 200 yards, unless I had a pretty good improvised supported position.