My longest shot on a predator, a red fox, was right at 300 yards, as determined by the bullet drop compensator which put the bullet where I wanted it, based on my estimation (which happened to be correct for a change LOL)
But, I have shot groundhogs at slightly under 600 yards, lasered. It gets very difficult to hit groundhogs at over 500 yards. The bullets are dropping around 1 more inch for every 10 yards between 500 and 600 yards, making range estimation very critical.
But, I have a friend who doesn't like to shoot at them unless they are at least 400 yards away. He uses a .22-.243 AI and I have seen him kill groundhogs at over 800 yards, lasered. It takes some sighting shots, and reference to his ballistic tables, to calculate winddrift, mirage, and exact range, but he's usually real close in 3 - 4 shots. He shoots a lot of ammo when the wind is blowing for each groundhog killed, though.
Around here, the 6 mm X .284 and .25 06 are very popular for coyote hunting, where most are driven or dogged, rather than called. Long shots tend to be the rule rather than the exception.