Some journal databases will index some grey literature, check the subject discipline pages to find the relevant databases for you. There are also some databases that specifically index grey literature.
Analysis & Policy Observatory (APO) - Australian based collection that focuses on policy research, includes over 34,000 resources, including grey literature reports, articles and data.
MedNar - Medically focused web search portal, that is an alternative to Google. It searches across medical society websites, NIH resources, US government websites and patents.
OpenGrey - Bibliographic information on 700,000+ European Grey Literature references. Includes content on Science, Technology, Biomedical Science, Economics, Social Science an Humanities.
Science.gov - access to research and development results and scientific and technical information from scientific organisations across 13 federal agencies in the US
WorldCat that let you search library collections from 170 countries.
WorldWideScience.org - Like MedNar, this is a real time web search portal that searches across scientific databases and portals internationally.