Mario - like pretty much every other 2D platform star - runs from left to right. That's just the natural order of things, and has been since the platforming genre began decades ago. However, Mario's direction isn't just a stylistic choice; apparently, our brains prefer left to right movement.
Lancaster University psychologist Peter Walker is the man behind the theory, and he has analysed thousands of images of people and objects in motion in order to compile the journal Perception.
Here's what he said:
What artistic conventions are used to convey the motion of animate and inanimate items in still images, such as drawings and photographs? One graphic convention involves depicting items leaning forward into their movement, with greater leaning conveying greater speed. Another convention, revealed in the present study, involves depicting items moving from left to right.
Interestingly, this only seems to apply to moving objects, and not static images - like photographs. Walker's research would indicate that there's a "fundamental left-to-right bias for visual motion", and that means that Mario will always be better than his sibling.