These are freely available datasets from here and around the world. Some are accessible via API's, which are an automated way to mine data into software like Google Refine.
Data.gov.au -  Is hosted by the Australian Government. At present it contains over 1000 datasets, including datasets on Society, Community and Culture. Contains a bunch of interesting apps also.
Datacatalogs.org  - Is a portal to open Datasets from around the world. API compatible.
The David Rumsey Historical Map Collection  - This is a database of 32,000 maps and images, focusing on rare 18th and 19th century North and South American maps, though the rest of the world is also represented. This collection can be viewed in conjunction with 2D and 3D GIS software as well as Google Earth and Google Maps.
DSDR - Data Sharing for Demographic Research - At the University of Michigan. Contains a range of mineable demographic information from the US.
Eurostat  - Business and demographic statistics from the Eurozone. Also contains specialist datasets like Culture and Social Inclusion.
KEDS - Kansas Event Data System - From Kansas University. Uses automated coding of English language news stories in overseas locations to predict political change.
Statista  - A wonderful data portal with an easy to use search interface. Try searching for anything you like - 'internet shopping', 'US Elections', 'social media' and see what it can do!
World Bank Data Catalog  - A wealth of datasets from all parts of the globe. Contains World Development Indicators, World Bank Finances, Health, Education Stats and much much more! Largely API compatible.