Wristwatches are used by Muggles and wizards alike, but they have a special significance in the wizarding world as a traditional 17th-birthday gift. Ron received a new gold wristwatch from his parents for his seventeenth birthday (HBP19, DH7). On Harry’s seventeenth birthday, the Weasleys gave him a slightly damaged wristwatch that had belonged to Molly’s brother Fabian (DH7).
Dudley received a gold wristwatch on his eleventh birthday. Later that same day, Harry wished that he had a watch so that he could keep track of the time while confined to his cupboard (PS2). At the Hut on the Rock, Harry counts down to midnight by looking at Dudley's watch (PS3).
Harry either owned a wristwatch or acquired and used on as part of his disguise when he used Polyjuice Potion to become Goyle (CS12).
Harry definitely wore a wristwatch by the end of his third year (PA16, PA21), but Harry's watch stopped working after he wore it into the Lake during the Second Task of the Triwizard Tournament (GF27).