For the US; there is a fairly comprehensive collection geographic data sets available from the National Atlas http://www.nationalatlas.gov/atlasftp-1m.html all freely available and public domain. And of course the US Census http://www.census.gov/geo/maps-data/data/tiger.html TIGER/Line dataset.

The World Bank http://maps.worldbank.org/ has maps covering multiple economic indicators, coverage is uneven and it's mostly focused on the global south.

http://geocommons.com/ has a largish assortment of geodata but the curation and search functionality is a bit confusing and they require a login.

http://www.statsilk.com/maps/download-free-shapefile-maps has a number of pointers to other resources.

I needed a rather large test dataset for an aerial imagery basemap, so I went onto USGS's "EarthExplorer" web site [1].

If you need to fetch a lot of data, don't bother trying to download it through the website itself, instead place an order through the "bulk downloader" interface [2]. The order size is limited however, but it was incredibly easy to patch in a simple 'window.setinterval' script through the JS console to make it automatically generate orders from a particular search set.

1: http://earthexplorer.usgs.gov 2: http://earthexplorer.usgs.gov/bulk/help

To find geo data in Europe you can use: http://inspire-geoportal.ec.europa.eu/discovery/ There are a lot of thematics data from various countries.

Depends on what you need. Natural Earth is a great large scale PD dataset.