During the recent storm my neighbor’s tree fell in my back yard does he have to pay for its removal?
No, there neighbor is not obligated to remove the tree.
The reason for this is that although having a fallen tree in the yard might be considered “damage,” it is not damage that the neighbor could have foreseen or taken action to prevent. The storm is not a “common wind,” but a very uncommon and even unheard of wind, and therefore there is no onus on the neighbor to take care lest his tree cause damage by falling.
Because of this, he does not have an obligation to repair the damage caused by the tree.
Having said this, it remains good neighborly conduct to at least share in the expenses.