If a healthy tree fell on a neighbor's property with no damage, who is responsible?

Are you asking about responsibility for cleanup?  More information is needed to fully answer this question, but assuming that the landowner where the tree was planted did not make negligent or unreasonable use of his land causing the tree to fall or could not have taken any steps to prevent it from falling, then the neighbor is responsible for the cleanup.  However, because there was no damage and to be a good neighbor you should offer to at least split the costs of removal and perhaps even paying for it.  The cost of removal is not worth damaging your relationship with your neighbor.