"Then she met that Potter at school and they left and got married and had you..."
     -- Petunia Evans Dursley

The year 1980 was a momentous one. Lord Voldemort was taking over. His followers, the Death Eaters, were torturing and murdering those who stood against their master. There were casualties on both sides of the conflict. However, in the middle of the year, on July 31, a boy was born who would be the Wizarding World's one best hope for the defeat of Lord Voldemort forever.

Important events of 1980:

Professor Trelawney's first prediction (early in the year, possibly late in 1979)
Murder of Regulus Black by Death Eaters on Voldemort's orders (or at least that's the story as far as we now know it)
Capture of Karkaroff and Dolohov, who are sent to Azkaban
Deaths of Rosier and Wilkes at the hands of Aurors

Births:

March 1 - Ronald Bilius Weasley, to Molly and Arthur Weasley
June 5 - Draco Malfoy, to Lucius and Narcissa Malfoy
June 23 - Dudley Dursley, to Petunia and Vernon Dursley
July 30 - Neville Longbottom, to Alice and Frank Longbottom
July 31 - Harry James Potter, to Lily and James Potter

Ages:

Dumbledore is around 140
McGonagall is around 60
James, Lily, Snape, and their contemporaries: around 20-21
Bill Weasley: turns 10 on 
Charlie Weasley: turns 8 on
Percy Weasley: turns 4 on 
Fred and George Weasley: turn 2 on April 1
Hermione Granger: turns 1 on September 19
Lucius Malfoy: turns 26

Events in the Muggle world
July 31 - Jo Rowling turns