United Nations -- Data on the trade indicators related to the Millennium Development Goals is available at http://unstats.un.org/unsd/mi/mi_goals.asp . The United Nations also has a Commodity Trade Statistics Data Base that allows the user to search for trade in selected commodities by country and by year (from 1962). The data base is at http://comtrade.un.org/db/
World Bank -- The World Bank provides trade data in time series on its subscription data base World Development Indicators data base as well as a dedicated trade site --World Integrated Trade Solution -- at https://wits.worldbank.org/ which requires registration (free) for access to some of the data.
World Trade Organization (WTO) -- The WTO has a wealth of trade data on its website--international trade and tariff data is available at http://www.wto.org/english/res_e/statis_e/statis_e.htm . Links include an interactive statistics database, downloads of the International Trade Statistics reports starting in 1998, tariff data and downloads of staff working papers.
UNCTAD -- Provides a variety of data and graphs on trade and related issues at http://unctadstat.unctad.org/EN/ as well as facilities to download data at http://unctadstat.unctad.org/wds/ReportFolders/reportFolders.aspx?sCS_ChosenLang=en.
OECD-- Data on trade and a wide variety of other topics for the OECD countries is available at https://stats.oecd.org/