You realize this is a LONG RANGE HUNTING forum, right? It's not just a hunting forum...
Yes, I understand that. I have a military backgroieund, specifically infantry. I retired after 20 years of going to places for Uncle Sam and killing people that he said I should. I have worked with Army, Special Forces and some Delta and Marine Recon snipers. My youngest brother was a SF trained sniper. I started shooting in West Texas at the age of 12, and have continued until now. I still shoot prarie dogs at distances out to 500 yards with a 25-06 or a 6mm Remington. I regularly shoot steel 18 inch targets out to 600 yards, which is as far as the range I shoot on will allow. (They're talking about expanding to 1,000 yards) I shoot at this range with a Remington 700 heavy barrel .308, both Remington 300 winmags, both 30-06's and my 35 Whelen. I use Shepherd scopes on most of these rifles, and my buddy George works as a spotter for me in high wind conditions. I wouldn't take a shot past maybe 700 yards at game with any of these rifles, simply because of the possibility of wounding instead of killing my target. Have I taken shots longer that that? Yes, but not at big game.
As to a definition of long range, its going to be different for every hunter. I would say it is the farthest distance that an individual hunter and rifle combination is capable of hitting and killing his game animal cleanly. I have a friend in Kansas (retired Army) who wouldn't shoot past 150 yards at deer with his 30-06, and never took a running shot until he borrowed my 1903A3 and killed a doe across a wheatfield at a measured 305 yards with a 165 grain Hornaday bullet going about 2850fps at the muzzle. It was a perfect heart/lung shot and dropped the deer on the spot. The next year, he borrowed my Ruger M77MKII with Shepherd P2 scope in 30-06 and killed a deer at 450 yards on Fort Riley. the bullet used was a Sierra Gameking 180 grain at a chronographed 2680fps. The exit wound was about the size of a 50 cent piece. That's longrange for Gene. Now, the longest shot with the .308/7.62X51 was done in Faluja at 1,380 yards, and the sniper who made the shot was just trying to mess up the Iraqi sniper's aim. He didn't expect to hit, due to the limitations of the round he was using. As a highly experienced sniper, he considered it a very lucky shot. The snipers who make these shots beyond 1200 meters are extremely experienced, highly trained, and have ballistic calculators and range finders that are far more accurate and powerful than what is available on the civilian market, and they still have to take more than one shot to hit. And wounding at 1500 yards with anything less than a .338 caliber bullet (and a heavy one, at that) is a great way to lose game. Penetration suffers, the wound channel is only the size of the caliber, and the hit has to hit something vital to get a kill that isn't delayed by minutes to hours.
As to me mentioning the 45-70, and its various similar cartridges, up until Carlos Hathcock, the longest recorded shot in combat was made by Billy Dixon at Adobe Walls, Texas. By the way, I've been to Adobe Walls three times, just to stop at Billy's grave and look at the terrain where he made that shot. It was made with a 50-90 Sharps, probably loaded with a 500 grain bullet and about 110 grains of black powder, and it was 1,580 yards. He killed one of Quana Parker's sub-chiefs. The shot was measured by the Army Corps of Engineers. Billy Dixon was one of about 8 civilians ever awarded the Medal of Honor, and it was for his accurate fire at the Buffalo Wallow fight, later that year. I know the shot was made and I know it was made at that distance, and I know it killed the sub-chief because I knew Deayne Parker, who was Quana's grandson. Just because a rifle will reach 1500 yards doesn't mean you should try to kill game at that distance with it. You have to take into account the limitations of the round, terrain, conditions and your own skill. I'm good for about 800 yards, right now, but my .300 winmag is only good as far as the bullet will perform consistently, which is about 450 yards on Elk. Sorry.