All guns have the potential to burn out their barrels over time.
The question is, how much time do you have on your hands?
Reduced to it's smallest denominator, rifle barrel life is proportionate to the total pounds of powder you burn through it.
Think about it.
A .22 Long Rifle burns maybe a few grains of powder with each shot. It's hardly a barrel-burner.
A .308 Winchester burns about 42 grains of powder with each shot. The cartridge is known to keep barrel accuracy and life through several thousand rounds before tapering off due to throat erosion.
A 7mm Remington Magnum burns about 78 grains of powder with each shot. A rifle chambered for this round will have a shorter life than the .308 Winchester above, but it will still be a fairly long life assuming you don't do a lot of rapid-fire shooting that heats up the barrel without letting it cool down between shots. Lots of heat, and lots of powder granules sandblasting their way past the barrel throat as they ignite further down the barrel are no friend of a rifle.
A .30-378 Weatherby Magnum burns about 115 grains of powder with each shot. Barrel life for this round is measured in the hundreds. I've known guys who buy several barrels at a time for their .30-378 rifles, because a barrel swap in inevitable.
Another way to look at it is figure how many rounds of a given cartridge you can get from a pound of powder. The fewer rounds you get, like the big Weatherby listed above, the more prone to throat and barrel erosion you are.