Is the tree on top of your home, garage, or outbuilding? Homeowners insurance covers removal costs in this situation, and pays to repair structural damage. The policy deductible applies.
Homeowners insurance does not pay for debris removal unless the tree lands on top of a covered structure. This means you are likely on your own if the tree fell without damaging your home, garage, or outbuilding.
Keep in mind that you are not responsible for a neighbor's structural damage or clean up costs if your healthy tree ends up in the yard next door. Storms are 'Acts of God' beyond anyone's control. Your neighbor will need to make a claim through his/her homeowners insurance policy.
The same is true if someone else's healthy tree falls in your yard. If there is structural damage, make a claim on your own homeowners insurance policy. Otherwise, clean up costs are out-of-pocket.
Trees occasionally drop limbs on top of parked vehicles too. Homeowners insurance does not over vehicle damage. The car owner can make a claim with his/her auto insurance company if the vehicle has comprehensive coverage. The claim is subject to the comprehensive deductible. Those with liability-only insurance are on their own for vehcile repairs.