I've found that it can vary quite a bit. For example, my brother has a smoothbore 870 that shot pretty decent out to 75 yards or so. But my Winchester is not nearly as accurate- I switched to a muzzleloader because I couldn't hit anything past 50 yards with it. So some, but not all smoothbores can be accurate. But you're probably going to be limited to 80 yards or so, even with an accurate one.

A rifled barrel will generally be a lot more accurate, and it will extend your range out to 120 - 150 yards if you have a scope.