As stated, knowing your idea of long range and your intended purpose will be essential for making a good recommendation for a long range caliber.
Know whether or not you reload and what kind of budget constraints you have will also help individuals make appropriate recommendations. Do you have any problem with wildcats. How important is a flat trajectory (in other words is maximum point blank range important)?
Depending upon your platform the 7mm Remington Magnum can be an excellent long range cartridge.
I know people that look at 500m as long when Elk hunting.
That would include me.
Here are some general recommendations.
Starter rifle punching paper out to 1000 yards 308.
Excellent low recoil paper puncher out to 1000 yards: 6.5-284, 6.5-06.
Higher energy general purpose...good for paper beyond 1000 and good for long range hunting. 7mm Remington Mag, 30-338 Winchester, 300 Win Mag.
Real long range high energy rounds...338 Lapua, 50 BMG.
Long range hunting rounds for Deer sized game...25-06, 257 Weatherby, 6.5 Sweede, 264 Winchester Magnum, 270 Winchester, and 270 Winchester Short mag.
Long range big game calibers with a very flat trajectory could include the 264 Winchester Magnum, 270 Winchester Short Mag, 270 Weatherby, 7mm Remington Magnum, 7mm Weatherby, 7mm STW, 7mm RUM, 300 Winchester, 300 Weatherby, 300 RUM, 340 Weatherby.
This list is not inclusive I left out a number of great rounds that are either specialized or proprietary, and a great number of other calibers will work depending upon your percieved needs, your skill, your chosen platform, and to a great extent the situation around the hunt.
Let us know what you intend to do....Good luck.