No one, besides Lincoln, has ever done that. From the transition office:

On January 20th, President-elect Barack Obama will take the oath of office using the same Bible upon which President Lincoln was sworn in at his first inauguration. The Bible is currently part of the collections of the Library of Congress. Though there is no constitutional requirement for the use of a Bible during the swearing-in, Presidents have traditionally used Bibles for the ceremony, choosing a volume with personal or historical significance. President-elect Obama will be the first President sworn in using the Lincoln Bible since its initial use in 1861.
“President-elect Obama is deeply honored that the Library of Congress has made the Lincoln Bible available for use during his swearing-in,” said Presidential Inaugural Committee Executive Director Emmett Beliveau. “The President-elect is committed to holding an Inauguration that celebrates America’s unity, and the use of this historic Bible will provide a powerful connection to our common past and common heritage.”

The Senate has a useful website with information about inaugurations. Looking over it, the great majority of presidents in the last century have used family Bibles for their swearing-in. The ones who didn’t — Jimmy Carter and Warren G. Harding — chose a Bible used by George Washington. Dwight Eisenhower, in his first inauguration, used the Washington Bible but also his own Bible from West Point. (Just as there’s no requirement you use a Bible, there’s no requirement that it has to be just one Bible, although in his second inauguration Eisenhower used only the West Point Bible.)

Obviously, I buried the lead. It should have been “Obama Joins Distinguished Predecessors Harding and Carter in Choosing Bible Used By A Previous President.” (OK, Eisenhower too, but just half.)

UPDATE: I should add that I at first missed the fact that George H.W. Bush also did the two-Bible thing, with a family Bible and the Washington Bible. So add him to the Eisenhower category.