Depends on the rifle and sights.
My Mosin-Nagant? ...Umm.... 150 yards, maybe,
maybe 200. And that's probably max out of everything I currently own with iron sights.
The nearly-finished Marlin 444? ...Probably 125 yards, or so. The huge front post (Skinner wing sights) obscures the target quite a bit - I and I had this barrel chopped to 19" rather than the usual 22". So once you get out there much farther than 100 yards, even most of a deer disappears behind the post.
There are some other things in between, but on down the line...
The shortest distance at which I would max out on game would probably be the .475 Tremor (AR). Between cartridge ballistics (flying 275 gr ashtray at ~1,700 fps), sight radius (11.2"), and sight design (thick post), I'd he hard pressed to push it beyond 90-100 yards. --Even then, I'm already dealing with 6 inches of drop at 90 yards, and 7.6 inches at 100 yards (can you say, "Rainbow trajectory?").
And for
non-game animals, the shortest would be the AR pistol (.223) fired from the shoulder. The 7.5" barrel and short sight radius isn't very useful for much more than 50 yards. And even that is pushing it for some animals, since elevation adjustment can only be done one
half turn at a time, due to the type of front post that I'm using; which results in elevation only being adjustable in 4.4 MoA increments.