There are a few papers that I have seen that publish insiginficant results, such as responses (see Easterly's response published in the AER to Burnside and Dollars World Bank paper titled 'Aid, Policies and Growth). The aim of these papers, however, is to negate a positive claim which they do by producing insignificant results (in the hypothesis testing sense) using the same idea as the original authors, but using new data. However, I have yet to come across a major paper in its own right published in the top 5 journals that publishes results that are insignificant. This is a scary thought because when I do my own research, I always shudder before entering the regress y x command. Are there well known papers that publish insignificant results? Thanks!
This does not directly answer your question, but I will try to explain why I don't think that such well known papers exist.
If submitted I don't think that such a paper would be accepted by the top five journals. This is because the journals also compete to stay relevant, to give surprising information. The phenomenon is known as publication bias.
This was also a big problem for the medical community. The solution they arrived at is that they only accept trials if the trial and its hypothesis is reported to the authorities at the beginning of the trial. Because of this the result will be stored no matter what it is. Even though unsurprising results are unlikely to get much publicity, a researcher looking for them can find them. The same solution cannot work for economic regressions because running a regression on the same data always gives the same result. Hence false positives are not a result of lucky samples, but of tweeking the model to particular data.