According to Wikipedia…
Born on the same day/month/year:
Ingrid Arndt-Brauer, German politician
John Clark Gable, actor and son of Clark Gable
Olsen, Danish footballer
Slim Jim Phantom, American musician (Stray Cats) ; although, Mr. Phantom’s invidual WikiPage says he was born one day later.
Some of the more famous people born on the same day and month:
43 BC – Ovid, Roman poet (d. 17 AD)
1639 – Ivan Mazepa, Hetman of Ukraine (d. 1709) {he’s included because my favorite operatic duet is from Chaikovskiy’s Mazzepa}
1811 – Napoleon II, Emperor of the French and King of Rome (d. 1832)
1820 – Anna Sewell, author of Black Beauty
1828 – Henrik Ibsen, Norwegian writer (d. 1906)
1882 – René Coty, French President (d. 1962)
1904 – B. F. Skinner, American psychologist (d. 1990)
1906 – Ozzie Nelson, American bandleader and actor (d. 1975)
1907 – Ruby Muhammad, American matriarch of Black Islam (d. 2011)
1908 – Sir Michael Redgrave, English actor (d. 1985)
1911 – Alfonso García Robles, Mexican diplomat and Nobel laureate (d. 1991)
1917 – Vera Lynn, English actress and singer
1918 – Jack Barry, American TV host (d. 1984)
1918 – Marian McPartland, British jazz pianist
1920 – Pamela Harriman, British-American diplomat (d. 1997)
1921 – Sister Rosetta Tharpe, American singer (d. 1973)
1922 – Ray Goulding, American comedian (d. 1990)
1922 – Carl Reiner, American film director
1925 – John Ehrlichman, American political figure (d. 1999)
1928 – Fred Rogers, American TV host (d. 2003)
1929 – Germán Robles, Spanish actor {“Timoteo de Salamanca” in Pasión (2007)}
1931 – Hal Linden, American actor
1939 – Brian Mulroney, former Prime Minister of Canada
1945 – Pat Riley, American basketball player and coach
1948 – John de Lancie, American actor {“Q” on Star Trek:TNG}
1948 – Bobby Orr, Canadian ice hockey player
1950 – William Hurt, American actor
1950 – Carl Palmer, English drummer (Emerson, Lake & Palmer)
1957 – Spike Lee, American film director
1957 – Theresa Russell, American actress {one of my favorite actresses}
1979 – Freema Agyeman, British actress {“Marth Jones” on Doctor Who}
I don’t share my exact birthday with anyone famous, but Janet Jackson and Tori Spelling were born on my birthday in later years.
Alex Salmond, Scottish politician
Hermann Tilke, German racing circuit architect
I’ve never heard of them!
But I have heard of our mod twickster! That’s why we sometimes call each other “twin” although we’ve never met!.
And Denzel Washington is just three days older than us. Hands off, oh you of the jackboots, I saw him first!
I was born on the same day as the chick who became the Queen of England…
I wanted to be a Queen! Liz stole MY life!
A bunch of " former footballers" and same day but not year Dragnets Jack Webb.
Not my birthday but…
I’m a huge Zeppelin fan, so when my daughter was born on Aug 20, it made an already awesome day a really cool day because it was Robert Plant’s birthday! 
Wil Wheaton
Same day for me, not year…
September 16
B. B. King
Lauren Bacall
Alexis Bledel
Amy Poehler
same exact day (9/16/70)
Anthony Marshall, NFL safety (Chic Bears)
Paul Shuey, Lima OH, pitcher (Cleveland Indians)
Mark Schultz, American musician
I did not replace anyone on the exact day I was born…Mary Travers (Peter Paul and Mary) died on my 39th. 
Stock market was bombed on my birthday in 1920, several devastating hurricanes hit on my birthday in many years…I clearly recall several years of not having power on my birthday and my mother telling me that I was so lucky “because everyone was lighting candles for my birthday!”