On game: 600-650 yards. Called the left eye on a doe antelope. .270 Win Winchester M70 Featherweight (borrowed), w/ 2-7x Leupold. Unknown handload w/ 130 gr SP (rifle owner's load - he told me where it hit at 100 yd, and that was it). One shot. Left eye.
I wouldn't do it again. Too dumb. Too risky. Too many variables. Good learning experience.
On targets:
I've had hits at longer ranges, but a recent, memorable instance is fresher in my brain:
~1,000 yards. .30-06, 6x45mm, and a couple others. We thought it was a small plate (~6-8") at 625 yards, because that's what the range owner told us. No, it was a very small (4") plate at just shy of 1,000 yards. It took me the better part of a 20-round magazine to walk the 6x45mm in with varmint bullets; and four rounds before the '06 connected. Things just didn't add up. Couldn't figure it out. Then we got home, took a look at satellite imagery, and found that the yardage was dramatically different than advertised.
Even on well-developed, well-maintained ranges controlled by a single owner, you can't believe anything you're told...
It was very cool watching my brother smack that tiny plate repeatedly with his .300 WM, though. Of 20 rounds fired, I believe 15-16 were hits.