Yes, Inauguration Day normally takes place on my birthday, January 20th. Technically, it still does. President Obama will be officially sworn in for his second term as President tomorrow at noon.
However, because January 20th falls on a Sunday this year, the ceremonial swearing-in of the President and Vice President, as well as all of the other inaugural activities, will take place on Monday. The postponement of inaugural activities because of the Sabbath has happened numerous times throughout history — both when Inaugural Day was originally March 4th: 1821 (James Monroe), 1849 (Zachary Taylor), 1877 (Rutherford B. Hayes), 1917 (Woodrow Wilson) and after it was switched to January 20th (in 1937): 1957 (Dwight D. Eisenhower), 1985 (Ronald Reagan), and, now, 2013 (Obama).
Random fun fact: That official swearing-in of Ronald Reagan for his second term on Sunday, January 20, 1985 is my first Presidential memory. Reagan had taken the official oath earlier that day and later did the coin-flip via satellite from the White House for the Super Bowl between the San Francisco 49ers and Miami Dolphins.