Effective range all depends on what you are intending to do. For hunting, very few situations will allow a responsible, ethical hunter to take a shot at anything over about 400 yards. Those who REALLY know their rifle, load, the exact range, ballistics for the given conditions (drop and drift will vary with temperature, barometric pressure, humidity, wind speed and direction) and such are the only ones that should take such shots. Even then, few rifles will be able to humanely and reliably kill an animal like a deer, never mind elk and moose, at ranges beyond about 600-800 yards even with a perfectly placed shot.
Target shooters on the other hand, are limited by the skill they possess and quality of their equipment. 1000 yards is certainly reasonable to use an '06 at for target purposes assuming rifle, ammo, and shooter are all up to the task.
As mentioned earlier, the '06 will certainly fly over 3 miles, if fired at about a 35-40 degree angle upwards with no obstructions until reaching ground level. Of course, hitting anything (even the broad side of a barn) intentionally at that range is nearly impossible.
I recall an incident near Eugene, Oregon where a man was out fishing in a boat in the Willamette River with his son, possibly also with a fishing guide or some other adult. While casting his arm jerked and he lost his rod. Turns out he'd been hit in the forearm with a .30 cal FMJ rifle bullet. It lodged in his arm after being fired from an estimated 3 miles away. They never determined who the shooter was. Luckilly the wound did no serious lasting damage.