If a tree growing in my yard, falls in my neighbor's yard, who is legally responsible to pay for it's removal ?

You are... its your tree plus any damages caused on neighboors property is your "bill" as well.

I would like to express a fact rather than a opinion here. There are many folks who have logical opinions but law does not always follow logic. If you have a tree on your side of the line and it falls on your neighbors side of the line the neighbor now owns that tree and the damage it has caused. If you cut the tree and caused this to happen you may have some exposure but if it fell by natural causes you are off the hook. If you want to find out which one of us is correct just ask your insurance agent.