Is there a list of large-scale, free datasets with psychological variables?
Participants at the last meeting of the Society for the Improvement of Psychological Science developed a list of >100 such datasets with some metadata such as topic, country, total number of participants, etc. The list is currently a collaborative wiki open to editing by anyone.

List of open psychology datasets and aggregators

Outside of psychology, there are a vast amount of aggregators. Here are two major resources:

https://www.quora.com/Data/Where-can-I-find-large-datasets-open-to-the-public

https://toolbox.google.com/datasetsearch