AppleCare for Macs, displays, iPods, and AppleTVs is international, although the AppleCare still has to be purchased in the same country that the product was.
As others have pointed out, hardware service for iPhones is generally required to be done in the country the iPhone came from. My guess this is because of the ~90 different countries the iPhone is sold in, most are SIM-locked to specific carriers, and the stores would have to stock replacements from each country in order to be able to offer international service. 😕