There isn't a simple answer to this question. It often depends on the risk of damaging property or causing injury. If the tree is in a wooded area and does not risk injuring anyone or damaging your property, you might choose to not cut it down at all. If the tree is hanging over your home or driveway and begins to decline, dropping branches, you may choose to remove it for safety reasons. Trees can sometimes survive for decades when broken or damaged, whether or not you remove it depends more on human factors. 

If you are concerned about the health of your tree and if it should be removed, I would recommend having an arborist come out and look at it. Certified arborists can be found at the following website.

https://www.treesaregood.org/