Some useful links to repositories concerning Climatic Datasets. The list is by no means exhaustive, it is just indicative.
If you know of any other related datasets, please let me know by e-mailing me at email@example.com. Thanks!
1. WorldClim: The dataset consists of gridded station data, that have been interpolated using splines interpolation method, implemented in the ANUCLIM software. The WorldClim climatology refers to the period 1950-2000 and has a world-wide coverage. You can find more details on the Hijmans et. al., 2005 and the Fick and Hijmans, 2017 papers.
2. E-obs: The dataset consists of station observations that have been interpolated using geostatistical methods. Their temporal coverage extends back to 1950 and goes right until 2017, with a daily temporal resolution. The available variables are: daily mean temperature (TG), daily minimum temperature (TN), daily maximum temperature (TX), daily precipitation sum (RR) and daily averaged sea level pressure (PP). This dataset has been extensively used for model validation purposes. Its geographic extent covers the area of Europe. More information about E-obs can be found in the van den Besselaar et al., 2011 paper.
3. CRU: The dataset consists of interpolated station data and has a global coverage. The dataset is produced in the Climatic Research Unit (hence: CRU) at the University of East Anglia in the UK. Their available variables are quite many so you could rather check their website. The dataset is updated and the basic methodology has been re-visited through the course of this project, so more than one papers have been released, but maybe, you could start from this one: New et al., 2000.
4. FAOCLIM: The dataset consists of interpolated stations with a global coverage and includes up to 14 observed and computed agroclimatic parameters. FAOCLIM is a project of the Food and Agriculture Organization of the United Nations and emphasizes on the use of climatic information for agricultural applications. The FAOCLIM climatology covers the period 1961-90.
5. PRISM: The datasets consists of interpolated station observations, primarily focusing on the region of United States. The PRISM climatologies cover the period 1981-2010. You can find more about PRISM in Johnson et al., 2000 and Daly, 2006.
6. ERA-Interim: The ERA datasets are the reanalysis products of the European Center for Medium-Range Weather Forecast (ECMWF) and they consist of observational and model output data that have undergone the process of data assimilation, using the Cy31r1 Integrated Forecasting System (IFS) of the ECMWF. The ERA datasets extend back to 1979 and they are available for all 4 prognostic cycles. You can find more about the ERA reanalysis datasets in Dee et al., 2011.
7. ESGF: Ok, now this is massive! The Earth System Grid Federation (ESGF) facilitates a gigantic system containing observational and model output data for the whole globe! Model runs operated in the context of CMIP5 and CORDEX initiatives can be accessed through the ESGF portals, for present and future climate.