I am trying to model plant productivity using climate data and need photosynthetically active radiation data.
The ratio between PAR and global horizontal irradiation (GHI) is relatively constant over time and space, so you might use the many existing sources for the latter and make the conversion yourself. SolarGIS is commercial and definitely one of the best sources for GHI, but there are public-domain sources too, such as NASA-SSE, CM-SAF, JRC-PVGIS, SWERA or IRENA. They have different spatial/temporal resolutions, and geographical limits.
Sources of PAR data (i.e., without the need for conversion just described) include satellite obs and reanalysis, e.g.
http://glcf.umd.edu/data/par/
http://www.bml.ucdavis.edu/boon/data_solar_par.html
http://disc.sci.gsfc.nasa.gov/hydrology/data-holdings/nldas-parameters/photo-active-radiation
http://gcmd.nasa.gov/KeywordSearch/Metadata.do?Portal=nasa_geo&KeywordPath=Parameters|ATMOSPHERE|ATMOSPHERIC+RADIATION|SHORTWAVE+RADIATION&OrigMetadataNode=GCMD&EntryId=NCAR_DS741.1&MetadataView=Full&MetadataType=0&lbnode=mdlb3
http://www.star.nesdis.noaa.gov/smcd/emb/gsip/pages/data.htm
Depending on your application, you can also search for fAPAR data (fraction of absorbed PAR).
Depending on exactly what you want, you may be able to use data from the World Radiation Data centre.
Often individual coutries have data sets; eg USA (NCDC); UK (BADC) etc, but not necessarily on a world basis.
It may be easier to purchase data (eg http://solargis.info/). [I cannot vouch for the data, and have no affiliation with the above company].
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