The president-elect traditionally takes the oath with his hand on a Bible. However, this is not a requirement -- Theodore Roosevelt took the oath in 1901 without swearing on a Bible.
http://usinfo.state.gov/special/inauguration/inauguration_oath.html
John Quincy Adams took the oath with his hand on a volume of law;
http://inaugural.senate.gov/history/chronology/jqadams1825.htm
Because the point of swearing on a Bible is not to show support for the Bible ?- it's intended to be a sign of taking the oath of office seriously by swearing on something important to you. It's akin to a blood oath, or "I swear on my mother's grave" or "cross my heart and hope to die."
So Christians swear on the Bible, because (the thinking goes) swearing on their religion makes them that much less likely to break their oath. But the oath, not the Bible, is the important thing.
And in that context, forcing a Jew or a Muslim or an atheist to swear on a Bible is not just obnoxious; it's pointless. Because to a Jew, for example, an oath sworn on a Bible is no more or less binding than an oath sworn on a telephone book.
Also, it's worth noting that the Founders provided the option of simply "affirming" their committment to their duties. And again, two presidents have done just that: Franklin Pierce and Herbert Hoover. This further demonstrates that the whole idea of "swearing on" something is simply a tradition, not something central to the process. Just like the words "So help me God" that most presidents add to the end of the oath.
Further, I believe members of Congress take the oath en masse, and nobody checks to see if they're swearing on a Bible, Playboy magazine or nothing at all.
http://blogcritics.org/archives/2006/11/30/130521.php