James. James beats out both John and William, 6 to 4: James Madison, James Monroe, James Polk, James Buchanan, and James Garfield and, yes, James Earl "Jimmy" Carter.
Tied in second are the names William and John, both with 4 instances: William Henry Harrison, William McKinley, William Howard Taft, and William Jefferson Clinton. The Johns are: John Adams, John Quincy Adams, John Tyler and John Fitzgerald Kennedy.
George is third, with 3 instances, thanks to the both Bushes, who were the only George's besides George Washington. Andrew has 2 instances, Andrew Jackson and Andrew Johnson, as does Franklin, Franklin Pierce and Franklin D. Roosevelt.
Most unique names, besides Barack, are: Millard Fillmore, our little known 13th president, Ulysses S. Grant and Chester A. Arthur (in the author's subjective opinion). For most popular baby names, check here.