I say it really depends on your skill, how you feel at the time, the conditions and how the animal is acting.

Me personally;

Bow I like to limit myself to 25 yards or so. And I am talking about known yardages, not guessing. I might try a 30 or 40 yard shot if the conditions were perfect, I knew the yardage and the deer was very relaxed offering a very high percentage shot angle.

If I'm not sure about the yardage it would have to be 20 and in since that is about the farthest I judge well by eye.

With a shotgun, that would depend on which gun and the weather conditions. If it is windy or raining I won't shoot near as far. With my dedictated slug on a decent day 100-120 yards at this moment because that is where I know my gun is accurate to and I trust it. With my smooth bore probably 70 or 80 yards on a relaxed deer. It is fairly accurate out to 100 but I don't know if I trust it just yet.

With my Inline Muzzle loader I will shoot out to 150 yards. It is sighted in at 130 yards and will shoot point blank (3 inches high to 3 inches low from 25 to 150 yards) out to that distance. I get around 3 inch groups at 150 yards with it.

I don't own a centerfire and they are not legal in my area of Michigan so I don't know. I suppose if I were to hunt up north I would probably get a .243 and limit myself to 200 yards with decent ammo and good shot placement. Providing the gun was accurate enough at that range, which I don't see why it wouldn't be.

P dogs with my 17 HMR about 130-140 yards with V-max ammo on a calm day.

I will not shoot at a running deer regardless of weapon or range. It isn't something I practice so I will not try it in the field.

I agree with the others, if I don't feel 100% I can make the shot I don't pull the trigger.

Paul