Many articles, such as this one, report a significant wage gap between men and women of 15% or more as evidence of discrimination. On the other hand, some sources, such as this one, claim that the gap can be explained by factors such as the following:
Is there a significant difference in wages between men and women in first world countries that is not due to factors relevant to the job?
I can only give an example for developed countries. In the Ny Times article Why the Earnings Gender Gap in Business? Women Work Less from 2009 they cite research on MBA couples, and it's argued that wages remain largely the same among MBA holders up until the first child. After which most mothers (who continue their careers) are affected more than fathers when trying to balance motherhood and work.
Similarly in We did it! - The rich world’s quiet revolution: women are gradually taking over the workplace from the Economist also from 2009 argues that women who do well in their careers in their 20's, disappear in their 30's because they have to choose between motherhood and the career.
In the same issue of the Economist they give the statistics in the article Female power - Across the rich world more women are working than ever before. Coping with this change will be one of the great challenges of the coming decades:
Another American study, this time of women who left work to have children, found that all but 7% of them wanted to return to work. Only 74% managed to return, and just 40% returned to full-time jobs.
There are other differences between men and women in modern times that should create a shift in wages. In Sweden (my home country) 60% of university students are women according to the national university review of 2008 (in Swedish, sorry), and women typically do better than men in school {citation needed?}. I would argue that if university graduates earn more than non-graduates in the same job then womens wages will progress to the point where they overtake men if the above mentioned issue isn't a factor.
Some support that things have changed for women since 1970 was recently shown in Marginal revolution (a blog by two well published economists) where they plotted GDP in America together with the median wage by gender. They showed that while womens wages closely follow GDP, males wages have stagnated. If true this would mean that women are closing the income gap on males at the rate that the GDP changes.
More recently in 2015 a German newspaper reported on a German study that women work 23% fewer hours than men, with a wage gap of 22%. The work week difference of 7 hours doubles to a difference of 15 hours once there's children. It also says that of women with children 70% work part-time twice the amount of those without. Interestingly for men in Germany the change happens in the other direction where 6% of men with children work part-time, as opposed to 10% of those without. My German isn't good enough to read the original study for the researchers thoughts, but it seems to suggest that the wage gap in Germany is explained by the number of hours worked as opposed to wage discrimination.
I don't have a better answer than this, but I hope I've added a some food for others.
TL;DR
Women start earning less when they get children because they value parenting more.
If we are merely concerned with women as a whole demographic being underpaid then I would expect that they are going to rise above men as a whole demographic as we are graduating women in larger numbers and with better grades, which is a fairly recent happening.
The short answer is YES -- while some of the wage gap can be explained by choices, not all of it can.
According to the American Association of University Women:
After accounting for college major, occupation, industry, sector, hours worked, workplace flexibility, experience, educational attainment, enrollment status, GPA, institution selectivity, age, race/ethnicity, region, marital status, and number of children, a 5 percent difference in the earnings of male and female college graduates one year after graduation was still unexplained.
A similar analysis of full-time workers 10 years after college graduation found a 12 percent unexplained difference in earnings. [emphasis in original]
Much more information, including information about the pay gap in many different countries can be found by following the links on this page from Radford University.
A chart from the U.S. Senate breaks down the pay gap into explained (by factors such as hours worked and experience) and unexplained. This is the Government Accounting Office report that explains where that chart comes from.
You can also see similar analysis in What Do Wage Differentials Tell Us about Labor Market Discrimination? from the National Bureau of Economic Research. A similar analysis from a nonprofit working to expand opportunities for women in business found similar results in 2010.
The statistics of the matter pretty much agree (at least here in the UK) that women are statistically paid less than men.
This December 2010 post from the ONS describes the relevant statistics of the matter here in the UK.
I can't speak much about the reasons behind the gender wage gap without being too speculative, but one interesting paragraph from the article leaps out:
The scale and direction of the gender pay gap varies according to age. For instance in the 22–29 age group, full-time women earned 2.1 per cent more than full-time men and part-time women earned 1.7 per cent more than part-time men. The largest pay gaps in favour of men for full-time and part-time employees were in the 50–59 age group at 17.0 per cent and 17.4 per cent respectively. The largest pay gap for all employees, 27.4 per cent, was seen in both the 40–49 and 50–59 age groups.
This suggests that the pay gap is directly related to age, and among younger people is largely disappearing.
According to this article in Time magazine, unmarried, childless women under 30 who live in cities earn more money than men in the same position. They postulate the cause is a greater number of women earning college degrees. Doesn't directly answer the question, but interesting, nonetheless.
This answer only relates to one first world country, Sweden, but it does provide a tangible case. Sadly, I could only find the source below published in Swedish, but since there were many answers referring primarily to newspapers I wanted to provide an answer using a primary source.
http://www.mi.se/files/PDF-er/att_bestalla/loneskillnader/skillnaden14.pdf
This report uses statistics from Statistiska Centralbyrån (Central Bureau of Statistics, a government authority) and Medlingsinstitutet (Swedish National Mediation Office, also a government authority), and is published by the latter.
On page 18 of the report, we can see the weighted statistics for 2014. It breaks women's pay down as a percent of men's pay by sector. The orange line is all sectors, the peach colored lines are private and public sectors respectively. Under private, we have the categories labourer and I'm not certain of the proper translation, but non-labourers essentially. Under public sector, it's broken down over municipality, county and state level.
The weighing takes age, profession, education, and working hours. After this weighing, women earn about 95% of what men earn on average. Private non-labour is by far the worst (91.9%) and municipality is by far the best (99.5%), both straying away from the average quite a bit more than the other sectors.
It should also be mentioned that the report's second chapter discusses a decrease in differences since 2008; 2.4 points as the unweighted average (between 1.4 and 4.2 depending on sector, the lower score being private labour and higher one being state level). The segregation by profession has also decreased. The report cautions comparing the values too much, though, as a different method was used prior to 2014.
The report doesn't further discuss possible reasons for the unexplained difference after weighing.
So, to summarize: Yes, women are, on average, underpaid in at least one first world country. It does seem fairly safe to assume this would be the case for many other first world countries as well, though that is of course speculation on my part as I provide no sources for that. Along with Martha F's answer, we at least have two.
These reports are created yearly and more of them can be found here: http://www.mi.se/publicerat/loneskillnader-mellan-kvinnor-och-man/
