IDEAS: Probably the largest database of economic research papers (both journal articles and working papers), with various rankings and cross-references

SSRN: Social Science Research Network. Aiming to facilitate rapid worldwide dissemination of research

JSTOR: One of the most well-known databases of journal articles. Papers enter this database a few years after their publication, so you have to search for most recent ones elsewhere. Access available at the WSE

NBER: National Bureau of Economic Research working papers. A lot of stuff published there eventually appears (usually with a lag of one, two or even more years) in the leading academic journals

IMF: International Monetary Fund working papers. Top-quality, timely, policy-oriented research

ECB, FED, BoE, BoC, Riksbank, RBNZ: Working papers of leading central banks

PWT: Penn World Tables. One of the most popular and comprehensive (in terms of country coverage) database for cross-country income comparisons

GapMinder: A fascinating trip through various development indicators, with animations

TED: Total Economy Database. Initiated by the Groningen Growth and Development Centre, currently maintained by The Conference Board. Data on output and productivity for over 120 countries

Maddison: Agnus Maddison's famous estimates of output, population and output per capita from 1 AD to present

EU-KLEMS: Excellent database for analyzing economic growth, productivity, employment creation, capital formation and technological change at the industry level. Includes all EU countries, the US and Japan

WB: Databases of the World Bank. Plenty of development indicators

IMF: Databases of the International Monetary Fund. Plenty of statistics, including international trade, capital flows, external debt, government finance etc.

OECD: Databases of the Organisation for Economic Cooperation and Development. Plenty of statistics, including international trade, research and development expenditures, structural indicators etc. Available via a trial-period arrangement

Eurostat: The first address for EU statistics

BIS: Databases of the Bank of International Settlements. A unique source of banking, payment, exchange rate, external debt statistics and more

Dynare: A very popular collection of routines (usually used with Matlab/Octave) for solving non-linear models with forward-looking variables. An excellent achievement by the team led by Michel Julliard at CEPREMAP, making DSGE modelling accessible even for non-experts in programming

DSGE-NET: International research network for DSGE modelling

Schorfheide: Frank Schorfheide's homepage, with (mostly GAUSS) codes replicating the main results of his research papers

Ireland: Peter Ireland's homepage, with Matlab codes replicating the main results of his research papers