Traditionally, a man should wear his watch on the wrist that is opposite of his dominant hand. In other words, a man who is right-handed should wear his watch on his left wrist.
Whether a watch is worn on the left wrist or right wrist is entirely up to the individual. Tradition dictates that the watch should rest at the tip of the bone that sticks up from the wrist. The watch should be worn loosely to allow for ease of movement.
Movement is one possible reason behind wearing a watch on the non-dominant hand. By doing so, the watch is subjected to a lesser amount of movement and thus less likely to be broken. Additionally, wearing a watch on the non-dominant hand makes winding the watch easier. It also allows for a person to easily check the time while writing or performing other activities requiring the use of the dominant hand.