Any wind speed could blow things around and cause a bit of damage but for the wind to really cause damage the wind speed would have to be 50 MPH to 80 MPH or above.
Any wind speed at 50 MPH or above you can expect damage to be done to roofs, and other things.
When the wind is forecast to be blowing hard make sure you put any lawn chairs or any other thing that's outside inside to avoid it being blown around and potentially injuring someone or causing damage.
When the wind speed gets up to 100 MPH or above you can expect severe damage to things such as structures trees and anything else in it's path.