January 9 = Severus Snape (1960)
January 26 = Gilderoy Lockhart (Pm)
January 30 = Lily Potter (DH) (1960)
February 6 = Arthur Weasley
February 13 = Luna Lovegood (JKR/Tw)
February 24 = Newt Scamander (WFT) (1897)
March 1 = Ron Weasley (1980)
March 9 = Sybill Trelawney (Pm)
March 10 = Remus Lupin (1960)
March 27 = James Potter (1960)
April 1 = Fred and George Weasley (1978)
April ? = Teddy Lupin (1998)
April 28 = Horace Slughorn (Pm)
May 2 = Victoire Weasley (YL)
May 15 = Pomona Sprout
June 5 = Draco Malfoy (BFT) (1980)
June 23 = Dudley Dursley (inferred from canon) (1980)
June 28 = Dobby
July 30 = Neville Longbottom (OP37, JKR) (1980)
July 31= Harry Potter (1980)
August 11 = Ginny Weasley (1981)
August 18 = Celestina Warbeck (Pm)
August 19 = Tina Goldstein (WFT) (1901)
August 22 = Percy Weasley (1976)
August 26 = Dolores Umbridge (Pm)
September 19 = Hermione Granger (1979)
September 25 = Garrick Ollivander (Pm)
September 26 = Quirinus Quirrell (Pm)
October 4 = Minerva McGonagall (1935)
October 17 = Filius Flitwick (JKR)
October ? (third week) = Angelina Johnson (GF16)
October 30 = Molly Weasley (c. 1950)
November 3 = Sirius Black
November 22 = Silvanus Kettleburn (Pm)
November 29 = Bill Weasley (1970)
December 6 = Rubeus Hagrid (1928)
December 12 = Charlie Weasley (1972)
December 31 = Tom Marvolo Riddle (Lord Voldemort) (1926)
Besides the birthdates, there is more canon information we can gather from these:
- We learned, by order of the dates, that Hermione was either the eldest of the trio, or almost a year younger. Jo later confirmed that Hermione was older in her FAQ answer to the question from the Open Letter to J.K. Rowling.
- We have confirmation of the first names of Filius Flitwick and Pomona Sprout, which we surmised from their Trading Cards, but had not yet confirmed. (Another question on the Open Letter to J.K. Rowling.)
- We also had more information on determining the ages of the elder Weasley brothers, Bill, Charlie and Percy; and the age difference between them (months and years).
- We can assume that House-elves are born and note the date, since Dobby has a birthday.
Some of these birthdays appeared in canon, either in the books or in interviews, before Rowling systematically listed them on her website. These include Harry, Neville, Hermione, Ron, and Fred and George. Dudley's birthday can be worked out with about 99% certainty from the text of the first few chapters of PS.
Then on July 30, 2004 the Wizard of the Month calendar on Rowling's website changed to say Happy Birthday to Neville Longbottom. The next day, July 31st, it (of course) said Happy Birthday Harry Potter. These were the first birthdays displayed and started a year of anticipation as fans watched the calendar for more birth dates. Over the course of the next year, nineteen birthdates were announced (twenty if you count both Weasley twins), the last new one being Dobby on June 28, 2005. After that point, they simply repeated. The birthday greetings appeared automatically at midnight UK time and remained for 24 hours.
A few dates were added over the next decade as biographies written by Rowling were added to Pottermore. The date for Tina Goldstein is from the promotional material for the "Fantastic Beasts" film and has been deemed to be canon.
It's interesting that we know the birthdates for so many characters, even those as insignificant as Kettleburn, but we don't know that of Albus Dumbledore.