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.
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: