Here's a list of the characters and the known birthdates, given to us from J. K. Rowling.
January 9th - Severus Snape - Capricorn
January 26th - Gilderoy Lockhart - Aquarius
January 30th - Lily Evans Potter - Aquarius
February 6th - Arthur Weasley - Aquarius
February 13th - Luna Lovegood - Aquarius
March 1st - Ron Weasley - Pisces
March 9th - Sybill Trelawney - Pisces
March 10th - Remus Lupin - Pisces
March 27th - James Potter - Aries
April 1st - Fred & George Weasley - Aries
April 28th - Horace Slughorn - Taurus
May 1st - Griphook - Taurus
May 15th - Pomona Sprout - Taurus
June 5th - Draco Malfoy - Gemini
June 23rd - Dudley Dursley - Cancer
June 28th - Dobby - Cancer
July 30th - Neville Longbottom - Leo
July 31st - Harry Potter - Leo
August 11th - Ginny Weasley - Leo
August 22nd - Percy Weasley - Leo
August 26th - Dolores Umbridge - Virgo
September 19th - Hermione Granger - Virgo
September 25th - Garrick Ollivander - Libra
September 26th - Quirinus Quirrell - Libra
October 4th - Minerva McGonagall - Libra
October 17th - Filius Flitwick - Libra
October 30th - Molly Weasley - Scorpio
November 3rd - Sirius Black - Scorpio
November 29th - Bill Weasley - Sagittarius
December 6th- Rubeus Hagrid - Sagittarius
December 12th - Charlie Weasley - Sagittarius
Voldemort - December 31st - Capricorn
and those same birthdates in alphabetical order:
Black, Sirius - November 3rd - Scorpio
Dobby - June 28th - Cancer
Dursley, Dudley - June 23 rd - Cancer
Flitwick, Filius - October 17th - Libra
Granger, Hermione - September 19th - Virgo
Griphook - May 1st - Taurus
Hagrid, Rubeus - December 6th - Sagittarius
Lockhart, Gilderoy - January 26th - Aquarius
Longbottom, Neville - July 30th - Leo
Lovegood, Luna - February 13th - Aquarius
Lupin, Remus - March 10th - Pisces
Malfoy, Draco - June 5th - Gemini
McGonagall, Minerva - October 4th - Libra
Ollivander, Garrick - September 25th - Libra
Potter, Harry - July 31st - Leo
Potter, James - March 27th - Aries
Potter, Lily Evans - January 30th - Aquarius
Quirrell, Quirinus - September 26th - Libra
Slughorn, Horace - April 28th - Taurus
Snape, Severus - January 9th - Capricorn
Sprout, Pomona - May 15th - Taurus
Trelawney, Sybill - March 9th - Pisces
Umbridge, Dolores - August 26th - Virgo
Voldemort - December 31st - Capricorn
Weasley, Arthur - February 6th - Aquarius
Weasley, Bill - November 29th - Sagittarius
Weasley, Charlie - December 12th - Sagittarius
Weasley, Fred & George - April 1st - Aries
Weasley, Ginny - August 11th - Leo
Weasley, Molly - October 30th - Scorpio
Weasley, Percy - August 22nd - Leo
Weasley, Ron - March 1st - Pisces
January 9th - Severus Snape - Capricorn
January 26th - Gilderoy Lockhart - Aquarius
January 30th - Lily Evans Potter - Aquarius
February 6th - Arthur Weasley - Aquarius
February 13th - Luna Lovegood - Aquarius
March 1st - Ron Weasley - Pisces
March 9th - Sybill Trelawney - Pisces
March 10th - Remus Lupin - Pisces
March 27th - James Potter - Aries
April 1st - Fred & George Weasley - Aries
April 28th - Horace Slughorn - Taurus
May 1st - Griphook - Taurus
May 15th - Pomona Sprout - Taurus
June 5th - Draco Malfoy - Gemini
June 23rd - Dudley Dursley - Cancer
June 28th - Dobby - Cancer
July 30th - Neville Longbottom - Leo
July 31st - Harry Potter - Leo
August 11th - Ginny Weasley - Leo
August 22nd - Percy Weasley - Leo
August 26th - Dolores Umbridge - Virgo
September 19th - Hermione Granger - Virgo
September 25th - Garrick Ollivander - Libra
September 26th - Quirinus Quirrell - Libra
October 4th - Minerva McGonagall - Libra
October 17th - Filius Flitwick - Libra
October 30th - Molly Weasley - Scorpio
November 3rd - Sirius Black - Scorpio
November 29th - Bill Weasley - Sagittarius
December 6th- Rubeus Hagrid - Sagittarius
December 12th - Charlie Weasley - Sagittarius
Voldemort - December 31st - Capricorn
and those same birthdates in alphabetical order:
Black, Sirius - November 3rd - Scorpio
Dobby - June 28th - Cancer
Dursley, Dudley - June 23 rd - Cancer
Flitwick, Filius - October 17th - Libra
Granger, Hermione - September 19th - Virgo
Griphook - May 1st - Taurus
Hagrid, Rubeus - December 6th - Sagittarius
Lockhart, Gilderoy - January 26th - Aquarius
Longbottom, Neville - July 30th - Leo
Lovegood, Luna - February 13th - Aquarius
Lupin, Remus - March 10th - Pisces
Malfoy, Draco - June 5th - Gemini
McGonagall, Minerva - October 4th - Libra
Ollivander, Garrick - September 25th - Libra
Potter, Harry - July 31st - Leo
Potter, James - March 27th - Aries
Potter, Lily Evans - January 30th - Aquarius
Quirrell, Quirinus - September 26th - Libra
Slughorn, Horace - April 28th - Taurus
Snape, Severus - January 9th - Capricorn
Sprout, Pomona - May 15th - Taurus
Trelawney, Sybill - March 9th - Pisces
Umbridge, Dolores - August 26th - Virgo
Voldemort - December 31st - Capricorn
Weasley, Arthur - February 6th - Aquarius
Weasley, Bill - November 29th - Sagittarius
Weasley, Charlie - December 12th - Sagittarius
Weasley, Fred & George - April 1st - Aries
Weasley, Ginny - August 11th - Leo
Weasley, Molly - October 30th - Scorpio
Weasley, Percy - August 22nd - Leo
Weasley, Ron - March 1st - Pisces