Washington and Lee University
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Monthly mean temperature, pressure, precipitation, vapor pressure, and sunshine for approximately 2,000 surface data collection stations worldwide, back to 1948.
A variety of free data compilations. From the National Weather Service.
From the National Climatic Data Center.
Copies of daily national weather maps, dating back to 1871. You will need to download the DjVU plug-in (free) to view the maps.
Temperature and precipitation data for 2,000 cities worldwide.
Data from over 16,000 cities, plus states, provinces, and countries.
Records from 1971 to date. From the U.S. Department of Agriculture. Please note the additional options on the right side of the page: national summaries and state summaries.