There are many questions that are asked in regards to trees and the protection of their bark. What will and will not damage a tree is largely based on the age of the tree. One specific question is whether or not putting nails in a tree will damage it.
This could be a problem for younger trees. Depending on the size of the tree, a nail could interfere with the tree's ability to transfer water in nutrients throughout the plant itself. The bark could also be damaged which could make the tree more susceptible to disease or pest problems.
On the other hand, nails generally will not harm a mature tree. The bark would be thick enough to prevent nails from penetrating too deep into the tree. A tree would easily be able repair itself around the puncture. At the same time, if a nail is supporting a large amount of weight you could damage the bark (again making it more vulnerable to problems). You may want to make sure that the item that you are nailing will not cause extreme stress to the tree.
Damage to the bark can be caused by a number of things. Animals can damage bark by chewing on the bark or rubbing their antlers against a tree. Lawn mowers and other yard trimming equipment can also cause issues. Using a bark protector or wrap can help with these issues