But be careful in some countries (some Asian and Middle eastern countries) the apple shops do not sell the applecare

! Yes they will repair the mac if you have the warranty.
(from the AppleCare FAQ)
Q: Where can I purchase the AppleCare Protection Plan?
A: The AppleCare Protection Plan is available at the online Apple Store, Apple retail stores, and many Apple Authorized Resellers. Apple recommends that you purchase the AppleCare Protection Plan in your country of residence, because each AppleCare Protection Plan has terms and conditions specific to consumers of the country or region in which the plan is offered. Please see the AppleCare Protection Plan Terms and Conditions for complete details.
(and from the terms and conditions)
l. For Plans sold in the United States, Apple is AppleCare Service Company, Inc. an Arizona
corporation with its registered office at c/o CT Corporation System, 2394 East Camelback Road,
Phoenix, Arizona 85016, doing business in the state of Texas as Apple CSC, Inc., AppleCare
Service Company, Inc. is the legal and financial obligor of Plans sold in the United States. The
obligations of the provider under this service contract are backed by the full faith and credit of the
provider, AppleCare Service Company, Inc. For Plans sold in Canada, Apple is Apple Canada
Inc., 7495 Birchmount Road, Markham, Ontario, L3R 5G2, Canada. Apple Canada Inc. is the legal
and financial obligor for Plans sold in Canada.
so, while the 1 year limited warranty gives you worldwide support, there is still a catch with the applecare, being that it seems to be a totally separate company..
i would assume that all the countries that participate in applecare, each have their own "company" that deals with the plans that were purchased in that country.