Harry Potter's alarm clock was an alarm clock that he salvaged from the damaged and broken contents of The Smallest Bedroom after first moving there in the summer of 1991. It presumably once belonged to Dudley Dursley.
Harry Potter found and repaired the alarm clock. Determined to finally get a hold of one of his Hogwarts acceptance letters, he set the alarm clock for 6 A.M. in the hopes of having it wake him up early enough for him to catch the post before Vernon Dursley could get to it and burn the letter. Unfortunately, Vernon had the exact same idea and camped out in front of the door of 4 Privet Drive in a sleeping bag.
In the summer of 1996, this alarm clock ticked on Harry's windowsill as he slept on the night that Albus Dumbledore came to collect him, but it was the darkness caused by Dumbledore's deluminator that woke Harry at exactly 11 P.M., rather than the alarm clock.