Daniel Pipes has devoted an ongoing thread to this question (which is well worth reading in its entirety, as it dates back to 2007, and provides much insight), noting most recently:
Half of Americans do not see Obama as Christian: A national survey by Pew Research conducted June 28-July 9, 2012, among 2,973 adults, including 2,373 registered voters, finds that "17% of registered voters say that Obama is Muslim; 49% say he is Christian, while 31% say they do not know Obama's religion."
That amounts to an almost exact split between those who say he is Christian and those who do not. Pew notes that fewer respondents "say Obama is Christian – and more say he is Muslim – than did so in October 2008, near the end of the last presidential campaign. The increase since 2008 is particularly concentrated among conservative Republicans, about a third of whom (34%) describe the president as a Muslim." (July 26, 2012)
Comment: The change in Republican and especially conservative Republican attitudes bears note.
Pipes also cites a statement by Obama's half-brother, who says, "on the inside, Barack Obama is a Muslim." Obama's step-grandmother reportedly prays for Obama to convert to Islam.