One theory is that since most people are right handed, putting the watch on the left wrist made it easier to wind.
Now with batteries and stuff, there is no need to wind, but it seems to somehow be natural once you get started, or have ever had to actually wind a watch!
Buzz Aldrin (the 2nd man on the moon) is left handed and wears his on his right wrist. The astronauts were provided with Omega Speedmaster watches for the trip.
In a recent Omega Boutique display in NY of his adventures, he pointed out that the Omega Speedmaster watch in the life size display was on the wrong (left) wrist!
The Omega Speedmaster was also the first wrist watch worn on the moon. Neil Armstrong left his (same Omega) in the lunar module.