I'm right handed and wear watches on my left wrist.
The thought of a watch getting in the way if I wore one on my right wrist has never occured to me, as I've always understood the reason for wearing a watch on one's left wrist (regardless of handedness) is because the knob to adjust the time is always (well, I've never seen one that isn't) on the right-hand side of the watch. Using the knob to adjust the time is therefore far less awkward and difficult if wearing the watch on your left wrist; however, I do realise you can just take the watch off, so perhaps that point is moot.