If a neighbor's tree falls on my property and causes damages, who is financially responsible?

This is the kind of question that gets non-lawyers annoyed at lawyers. It seems so simple, yet we make it so complicated. If the neighbor knew or should have known that the tree might fall, then he is responsible. If there were overhanging branches that the damaged neighbor could have removed and that's what caused the tree to fall in that direction, then he is responsible. If it was a violent storm that knocked the tree over, then no one is "responsible" but the damaged party has to deal with his own loss. Finally, if it just happened to fall without warning, perhaps it coulld be argued either way, but I'd say it's the tree owner who is responsible, after all, it's his tree.