What public data sets are available that could used for correlation in bitcoin analytics? What data sets exist out there that can be used for engineers to perform statistical analysis against? Hopefully this data is not needing to be scraped, but is available in an importable format or API, though I am open to suggestions on data that APIs need to be written for.
Historic trade data is available from the Bitcoin Charts Market API
Bitcointalk.org forum stats, impression stats for ads, e.g. new member sign-ups per day
Google Trends data for bitcoin. (Can be exported as a CSV file with links at bottom of the page)
Blockexplorer.com stats query page
Blockchain.info API
The Bitcoinstatus.RowIT page has graphs on the number of bitcoin hosts connected, client version and data on hosts/country. Don't see an API but some data is in tables so probably easy enough to scrape.
Chris Moore's answer to this question provides a lot of useful stats. 
Of course the blockchain itself.