The main sources of multi-sector data are the international organizations in the United Nations Family -- the main providers are the World Bank (IBRD), the United Nations (UN) and the United Nations Development Programme (UNDP). The World Resources Institute also provides multisectoral data, but with an emphasis on the Environment. Since April 2010 the World Bank has made all of its online databases available free, which makes it the first stop if you are looking for national time series data on any economic or social topic. Several organizations have data bases on specific Millennium Development Indicators, but the World Bank, and the UN have times series data on the indicators for all goals.
World Bank -- The most comprehensive set of multi-sector data is the World Bank's set of online databases. For more detailed information about the World Bank's suite of databases click here.
United Nations-- The major United Nations data base is the United Nations Common Data Base (UNCDB) with some time series going back to 1945. The UN also has a time series database of indicators developed to track the Millennium Development Goals (MDG) adopted by the UN and the World Bank. For more details on these databases click here.
United Nations Development Programme-- UNDP has greatly expanded the quantity of data available on its website. In addition to its flagship Human Development Indicators is now also publishes time series data on a number of related issues. For more information click here.
OECD-- Data on a wide variety of topics for the OECD countries is available at https://stats.oecd.org/
Gapminder -- Gapminder is an innovative data presentation web site which provides dynamic views of data changes over time using bubble graphs. Graphs are available for economic, population, health, environmental, agricultural and information technology data. Raw data can be downloaded from the site and a desktop version of the software is available free. Users can customize graphs using existing data, but cannot add new data. Much of the data used is from the World Bank and UN organizations. Gapminder is at http://www.gapminder.org .
World Resources Institute (WRI) -- WRI provides data on a wide range of resource issues. The data includes reports, data and maps in various formats. Many of the individual project reports include shapefiles-- but it is necessary to check the reports themselves to determine what type of data can be downloaded. The main link for data is http://www.wri.org/resources. One particularly useful set of shapefiles on water is included in the "Aquaduct" project reports--there are several of these reports and they usually include both spreadsheet data and shapefile downloads-- the shapefile package usually includes a pdf file which explains the data.There are many "Aquaduct" projects with shapefiles in the group "Maps". (Note that some downloads require filling in a request form to access the file.)
The Humanitarian Data Exchange -- This website put together by the UN Office for the Coordination of Humanitarian Affairs (OCHA) provides a collection of shapefiles, data sets, blogs, videos and other information-- all related in some way to humanitarian affairs. The collection is searchable. The website is at https://data.humdata.org/ .
Free GIS Data -- This website provides a list of more than 300 geographic data sets organized by category https://freegisdata.rtwilson.com/ . It also provides links to data for individual countries.
National Statistical Offices -- A list of links prepared by the United Nations to the websites of National Statistical Offices and other providers of statistics at the individual country level is available at http://unstats.un.org/unsd/methods/inter-natlinks/sd_natstat.asp and WTO also provides a list at http://www.wto.org/english/res_e/statis_e/natl_e.pdf .