I always thought regular game pads WERE left-handed. (Dominant hand controls the d-pad/stick.)
If you wanted a right hand controller, one of the few options was the Master System Stick.
I guess I don't know for a fact, but what I can tell you is that the majority of the population on Earth is right handed and that things are engineered for right handed people. If I had to guess I would say that gamepads are right handed.
My basis for this is that your dominant hand hits the buttons. Your dominant hand is able to handle multiple tasks like multiple buttons, turbo switches, etc. Your slave hand controls your movement. It doesn't have to do as much. I guess we could compare it to playing a guitar. If you play right handed, your left hand is on the frets, and your right hand does the strumming and picking.
[EDIT] Maybe left/right handed is not correct. I prefer having the buttons on the left. It's my preference and I'm able to hit the buttons more rapidly. Any time I ever visited an arcade I always used the buttons on the left (if available). If there weren't any, I crossed over my hands and played that way. I couldn't do this for fighter games, but I never was really any good at them any way.