It depends.
Small game with a .22 LR will be generally be within 50 yards, but I will go out to 100 if the situation call for it.
For mid-sized game I will use .223/5.56, generally within 100 yards, but will not hesitate to go out to 250.
For larger game I will use .308 and will generally be within 100 – 150 yards, but I will also readily go out to about 350 with it.
My range limits are certainly not based on the capabilities of the particular caliber, they are more based on the capabilities of my shooting.