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.
Eurostat - Business and demographic statistics from the Eurozone. Also contains specialist datasets like Culture and Social Inclusion.
Europeana - Europeana is a single access point to millions of books, paintings, films, museum objects and archival records that have been digitised throughout Europe. It is an authoritative source of information coming from European cultural and scientific institutions.
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.