Abraham Lincoln faces to the right on the penny, making him the only U.S. president on a coin that does that.
Sculptor Victor David Brenner, the designer of the penny, had previously sculpted a plaque based on a photograph taken of Lincoln in 1864. Lincoln faces right in the photo (which you can see here), so he also faces right in the plaque. When President Theodore Roosevelt hired Brenner to design the Lincoln penny in celebration of Lincoln's 100th birthday, Brenner based the penny off of the plaque he made, so he faces right on the penny.
On the 2005 nickels, Thomas Jefferson faces to the right too. Most nickels have Jefferson facing to the left, like the other presidents do on the other coins. However, in 2005 the nickel was redesigned to celebrate the Lewis and Clark expedition, and Jefferson was switched to facing right. Then, in 2006, the nickel was redesigned again, with Jefferson facing forward. This would make him the only U.S. president facing forward on a coin.