Removing upright-growing branches (water sprouts) is a good practice with most trees. Trees that naturally have upright growth of all branches should be allowed to develop naturally. There is no need to thin side branches the way we do with fruit trees. I usually remove a few branches that grow toward the center of the tree. I also remove some crossing branches unless the normal growth pattern is thick inner branch growth.
It is never a good idea to shorten the height of shade and evergreen trees. Occasionally branches that are growing toward structures are removed. In this case, it is usually best to remove the entire branch back to its origin. Pruning around utility lines is dangerous and is best left to professionals. If a tree becomes too large for the area where it is planted, the best practice is to remove it and plant a smaller tree.
Occasionally an extra long branch grows beyond the natural shape of a tree. It is usually best to shorten this branch back to a side branch which is just inside the natural outline of the tree.
Sometimes tree branches become broken and need to shortened or removed. The best place to shorten a branch is just above a smaller side branch. Branches that are larger than 3 inches in diameter should be removed in a three-cut method. The first cut is a partial undercut a few inches beyond the final cut. Then an overcut is made an inch or two beyond the first cut. If a heavy branch snaps as it is being cut, it will snap at the undercut.
Large branches have a shoulder a half-inch or so next to where they originate. This shoulder contains healing tissue to grow and cover the wound. If this half-inch of shoulder tissue is allowed to remain, the tree wound will heal much faster.