There are three main areas of interest when it comes to home insurance and trees. Your trees and shrubs are covered for losses due to risks like theft and fire, vandalism, but not wind damage. If you want wind coverage, you will need an additional rider.
The first question many people have is whether they have coverage if a tree falls and damages or destroys their roof. The answer is that most insurance policies do cover this. Your roof is a basic and important part of your home and it is generally fully insured minus the deductible.
The second question is: "What happens when a tree falls and blocks my driveway (or other part of my property)?" The answer to that one is more complicated. You generally need extra insurance to cover the trees and shrubs on your property if you want these removed. Sometimes coverage is adequate for removing the tree but not replacing it.
The third question is whether you are responsible for trees falling on your neighbor's house. If you were trimming the trees or performing some other task, your insurance is responsible. Another thing is if the tree was unhealthy and falls, you are responsible. However, if there is an "act of God" like a windstorm and a perfectly healthy tree were to fall, the other person's insurance would have to cover it.
If you have large trees on your property, you will want to have the necessary tree riders in your insurance policy. Trees can cause a great deal of damage and you want to be protected.
And, that's what you need to know about home insurance and trees.