Harry was born on July 31st of 1980. Up until his eleventh birthday, Harry never had a decent birthday. Sure, he'd get the occasional sock from the Dursleys, but Dudley's birthday was always far more celebrated then Harry's. That all changed on his eleventh birthday...
Just as the clock struck midnight on Harry's 11th birthday, something wonderful happened. A half giant named Hagrid stumbled into the "cabin" (more like shack) the Dursleys and Harry were staying in. From Hagrid, Harry learned more about his family and his past then he had living with the Dursleys for ten years.
Harry also received his first real birthday present. While purchasing supplies in Diagon Alley, Hagrid bought Harry's owl (Hedwig) for him.
Harry's 12th birthday, however, isn't much to write home about. None of the Dursley's made any notice of his birthday. Harry believed his friends have forgotten, only to find out that Dobby, a house elf, has been collecting Harry's letters. We never find out what was in those letters, nor what any of Harry's birthday greetings were.
Just an hour after midnight on his 13th birthday, three owls arrive at Harry's room, all bearing various packages.
From Ron, Harry receives his very first birthday card. He also gets a Pocket Sneakoscope, which is supposed light up when trickery is occurring near the orb.
Harry also receives a card from Hermione. She gives him a wonderful Broomstick Servicing Kit.
Hagrid also gives Harry a card, along with a gift. Hagrid gives Harry the new textbook for Care of Magical Creatures. The book is actually alive.
Harry's birthday is once again ignored by the Dursleys. However, he does receive four birthday cakes from Sirius, Hermione, Ron and Hagrid. These cakes are a huge delight to him because Aunt Petunia has put the whole family on a diet.
Not much is said about Harry's fifteenth birthday. We know he receives cards from Ron and Hermione. He also gets some Honeyduke chocolates from them, but in his frustration at being left the dark in regards to Voldemort, he throws them away.
For Harry's sixteenth birthday, a party is held at the Burrow with the Weasley family and Remus Lupin (and perhaps others). Not much else is said about this birthday, except that it was marred by grim news regarding new attacks and disappearances among the wizarding world.
Harry first celebrates his seventeenth birthday by using magic without fear of reprimand from the Ministry of Magic as the underage trace placed on him is now gone. He nearly pokes his eye out by summoning his glasses. Later, a party is held at The Burrow where they eat a giant snitch shaped cake. The mood of party is somewhat spoiled when the Minister of Magic arrives to question the trio about the mysterious items Albus Dumbledore left them in his will.
He does receive some interesting gifts, including a watch that belonged to Mrs. Weasley's brother, Fabian. According to Mrs. Weasley, it is tradition that wizards get watches when they come of age. He also receives a book called "Twelve Fail-Safe Ways to Charm Witches" from Ron, a new sneakoscope from Hermione, a box of the newest merchandise from Weasleys' Wizard Wheezes (courtesy of Fred and George, of course) and an enchanted razor from Bill and Fleur.