In some cultures people tend to wear a watch or ring on the right hand/wrist. I have met a few Muslims who tend to do this especially in the Gulf as the right hand is used for greeting, eating etc you walk into a house with your right foot and leave with your left. I have noticed on quite a few Arab programmes people wear their watch on the right wrist.
That of course is not everyone far from it, I have also met folk who just wear it on the left for the same reason most of us do, the right hand is the dominant hand so wearing a watch on it would be more likely to get in the way or get damaged.
Thats the only symbolism I can think of, possibly a religious one. Other than that perhaps left handed?