National Climate Data CenterYou can get yearly and monthly averages, search for data at particular locations, as well as get Global and U.S. Annual Climate reports. Data is sorted by method collected (i.e. weather balloon, marine and ocean, satellite, radar, etc.). My preference is to use the "Quick Links" feature to access data by category.
If you're looking for more specific regional datasets in the United States the best place to start is the NOAA Regional Climate Centers web site.