The data linked here consist of downscaled climate projections as part of CMIP3 and CMIP5, and gridded observed data that can be used in downscaling.
A library of downscaled climate projections, hosted by the Green Data Oasis provides many projections of future climate over the conterminous U.S. Streamflow was also derived as part of the USBR WaterSmart project with documentation developed with the USGS. Much of this data for the U.S. is also served by the USGS Geo Data Portal, along with many other data sets, both of observations and downscaled climate projections.
Old downscaled global CMIP3 GCM output are served here. This covers global land areas at a 1/2-degree (about 50 km) spatial resolution. A similar downscaled product using CMIP5 GCM runs is available at the same USBR site serving U.S.-based data.
Climate projections are also available at The Climate Wizard after post-processing to extract some statistics of precipitation and temperature.
There are a number of gridded data sets of observations for the U.S. and globally. One I have used extensively is the 1/16 degree daily gridded data of Livneh et al. available here.