I remember more than one argument with a friend over which way LEGO minifigures' hands should be oriented to be correct (with the thumb pointed upward/inward, like a human hand's neutral position).
This gentleman is holding his left hand so the rounded side faces down, and his right hand so the rounded side faces up. Is there an officially correct orientation? The peg connecting the hand angles slightly, so I've used both orientations in different situations to keep hands on steering wheels and control panels. Did I risk aggravating any minifigure's carpal tunnel syndrome in doing so?
Make a fist, and don't bend your wrist. The pinky's side of your hand is mostly aligned with the rest of your wrist and forearm. The thumb's side of your hand is not so much aligned with your wrist and forearm. Also notice that the curve of your fingers tapers toward the pinky finger.
Now compare to the minifigure hand. Notice that the wrist is closer to one side of the hand (the left hand in your photo) than the other.
I would generally agree with pcantin's answer, but there are some "official" cases where the right side is correct. Iron Man typically is in the "right hand" configuration, because it attaches translucent light blue circular 1x1 blocks to the bottom for repulsor beams. Also, the Frodo and Bilbo magnets both hold Sting pointed straight up, and do so using the "right hand" configuration, so their hands aren't high up in the air.