Data.gov.au - Is hosted by the Australian Government. At present it contains over 1000 datasets, including datasets on Construction materials, housing finance, planning, Property, and Transport. Contains a bunch of interesting apps and links to GIS software 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.
Eurostat - Business and demographic statistics from the Eurozone. Also contains specialist datasets like rural development and land cover/use.
Statista - A wonderful data portal with an easy to use search interface. Contains a wealth of economics data, including city liveability indexes.
TallyRoom Maps - These are downloadable map files for local and federal government land boundaries for Australia, Canada, the UK and New Zealand.
World Bank Data Catalog - A wealth of datasets from all parts of the globe. Contains World Development Indicators, Environmental stats, population forecasts and much much more! Largely API compatible
There is also an interesting web page here containing 20 free GIS tools