It's one of the questions our consumer advocacy staff expect after every winter storm: "Will insurance pay for damage from that tree that fell on my (garage, house, car, shed, fence, etc.)? And what if it was my neighbor's tree?"
The upshot: Most damage to buildings, vehicles and contents ARE covered by your standard homeowner's policy, even if it was your neighbor's tree. (Your insurer may try to get your neighbor's insurer to pay afterward. In those cases, you might get your deductible back.)
The bad news: Unless the tree hit a structure or is blocking your driveway, your insurer probably won't pay for removal of it.
Here's advice that's more detailed: The Insurance Information Institute recently put out a video explaining what's typically covered and by whom.