Economic data is a very broad concept. It can include discrete preference relation data-sets as well as extensive time series data.
But it is important that theories are tested against data, and the earlier this happens in the development of an economic model, or of a new economic hypothesis, the more beneficial will be to the researcher, providing early signals on how good or bad a match with the real world his theoretical endeavors are. Economics being a Social Science, it is also important to have plentiful of different data sets, since testing a theory on just one data set does not provide strong enough evidence of the model's usefulness or uselessness.
So I am posting this question with the hope that it will be gradually enhanced with answers and it will become a point of reference for Economic data of all sorts for this community.
My offering: The World Bank for example has very useful information on trade lanes. Other repositories: