Washing Windows Hanging Off a Rope; I Hope They Are Paid More Than Those Washing The Other Side
Here's one example of why men might earn more on average than women: they tend to far outnumber women in jobs that are very dangerous, and therefore highly-paid: coal mining, working on oil rigs, fishing, farming, logging, excavation, construction and window-washing, etc. I took the picture above of two window-washers hanging off the AEI building today on ropes, with no obvious safety equipment other than the normal-size ropes attached to something on the top of the building (notice the ropes aren't even visible in the picture!), with no buckets, trays or harnesses to support them, and nothing below them except the sidewalk to stop a fall. I'm pretty sure these guys make a higher wage than the maintenance workers who clean the same exact windows from the inside of the building.
Of course, there's nothing that would prevent women from becoming outside window-washers, but there might be natural gender differences in preferences for work environments that would discourage most women from hanging off a rope 10 stories above the street. Perhaps men show greater tolerance than women for risky, physically demanding, dangerous work in extreme outdoor conditions, and women put a higher priority on office work environments that are low-risk, indoors, safe and pleasant. Higher (lower) risk = higher (lower) wages, ceteris paribus, and women on average may be perfectly willing to accept lower wages for lower risk jobs, which would contribute to the wage gap.
Here's BLS data showing that in 2009, 93% of all workplace fatalities were men, and here's data showing that 90% of all fatal motorcycle accidents in 2009 were men, so I don't think there's any question that men are significantly more risk-tolerant than women. Any empirical study of wage differences by gender should control for risk and the probability of work-related injury or fatality, which I don't think usually happens.