“The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.”
— US Constitution, 20th Amendment
UPDATE:
Publicola: read the text of President Obama’s inaugural speech.
There was a lot of mention of God and faith in the speech, which has become pretty standard fare in modern American politics, but Obama did make a shout out to us “non-believers.” I don’t know for sure, but I’m guessing that might be a first for a presidential inauguration speech.