Is it legal to tackle a running back by there neck?

If you tackle them with your arm, yes. Shoulder no. If you tackle the arm it is known as a clothesline. It is a type of tackle made infamous by Dick "Night Train" Lane. Many players were injured using this type of tackle.

A majority of the time, if the hit is deemed vicious, it will be flagged for unnecessary roughness. If the tackle happens in the back of the neck and drags the player down (outside the tackle box), this is considered a horse-collar tackle, and it also a penalty.