http://www.ecmwf.int/en/research/climate-reanalysis/era-interim
A remodel of weather since 1979, based on many many measurements. The resulting dataset contains daily to hourly values around the globe for many meteorological and climatological parameters such as temperatures, water content, wind, radiation and various fluxes.
The most up to date version of this dataset is ERA 5: https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5

http://disc.sci.gsfc.nasa.gov/mdisc/data-holdings
A similar project as above the one above.

http://www.esrl.noaa.gov/ The Earth System Research Laboratory, with data and information or aerosols, as well as other temperature, precipitation etc. Within this organisation:

• http://www.esrl.noaa.gov/research/products/
• http://www.esrl.noaa.gov/psd/ (http://www.esrl.noaa.gov/psd/data)

(closed data) A commercial service that hosts a lot of high detail weather data, and allows a limited number (1000/day) of requests for free: https://darksky.net/

http://www.ecmwf.int/en/research/climate-reanalysis/era-interim
A remodel of weather since 1979, based on many many measurements. The resulting dataset contains daily to hourly values around the globe for many meteorological and climatological parameters such as temperatures, water content, wind, radiation and various fluxes.
The most up to date version of this dataset is ERA 5: https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5

http://disc.sci.gsfc.nasa.gov/mdisc/data-holdings
A project similar to ERA 5.

http://www.esrl.noaa.gov/ The Earth System Research Laboratory, with data and information or aerosols, as well as other temperature, precipitation etc. Within this organisation:

• http://www.esrl.noaa.gov/research/products/
• http://www.esrl.noaa.gov/psd/ (http://www.esrl.noaa.gov/psd/data)

(closed data) A commercial service that hosts a lot of high detail weather data, and allows a limited number (1000/day) of requests for free: https://darksky.net/. Darksky has been acquired by Apple and their API is no longer available.

http://www.ecmwf.int/en/research/climate-reanalysis/era-interim
  A remodel of weather since 1979, based on many many measurements. The resulting dataset contains daily to hourly values around the globe for many meteorological and climatological parameters such as temperatures, water content, wind, radiation and various fluxes.

http://disc.sci.gsfc.nasa.gov/mdisc/data-holdings
  A similar project as above the one above.

http://www.esrl.noaa.gov/ The Earth System Research Laboratory, with data and information or aerosols, as well as other temperature, precipitation etc. Within this organisation:

• http://www.esrl.noaa.gov/research/products/
• http://www.esrl.noaa.gov/psd/ (http://www.esrl.noaa.gov/psd/data)

http://www.ecmwf.int/en/research/climate-reanalysis/era-interim 
A remodel of weather since 1979, based on many many measurements. The resulting dataset contains daily to hourly values around the globe for many meteorological and climatological parameters such as temperatures, water content, wind, radiation and various fluxes.
The most up to date version of this dataset is ERA 5: https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5

http://disc.sci.gsfc.nasa.gov/mdisc/data-holdings 
A similar project as above the one above.

http://www.esrl.noaa.gov/ The Earth System Research Laboratory, with data and information or aerosols, as well as other temperature, precipitation etc. Within this organisation:

• http://www.esrl.noaa.gov/research/products/
• http://www.esrl.noaa.gov/psd/ (http://www.esrl.noaa.gov/psd/data)

(closed data) A commercial service that hosts a lot of high detail weather data, and allows a limited number (1000/day) of requests for free: https://darksky.net/