I tried to do some searching for some specific projects that I've heard of but I'm coming up blank.

Really any decent quantitative study that isn't just an absolute basic regression is going to have degree of data processing done to it. Not exciting, but it is there and on a large level.

The other more interesting projects are doing stuff like scraping news sources, constitutions, etc, using natural language processing to pick out relevant parts and then matching those to some kind of database in order to code the necessary data.

Here is an example of this: https://github.com/openeventdata/phoenix_pipeline

Then you've got something like Nate Silver's analysis and predictions of recent elections which is dealing with popular political issues + data.