Need to be very careful about this issue as it is multi faceted.
Firstly, Apples warranties for mobile products are subdivided by REGION - not COUNTRY. If you go to Apples Waaranty website http://www.apple.com/legal/warranty/products/ipad-english-mein.html
the first thing it asks you to do is say what REGION you purchased the item in (North America, Asia, Europe etc). Almost invariably, within this REGION you will be covered (Ipad bought in uk but used in Germany so covered by the European REGION would work etc etc).
There are real problems with a lack of international stadards when it comes cellular device networks making it virtually impossible to have a truly international waranty. As previous posters have mentioned, if the Apple store you take your mobile device to has a replacement that runs on the same cellular frequencies etc then they will most likely swap it out for you if you can prove purchase etc. However, more often than you would think, the standards of the local cellular networks are completely different making the ability to stock a broad enough range of replacements infeasibe and very costly. This is why so many people fall foul of international waranties for items bought from another country.
As has also been mentioned, if you stick to a WiFi only iPad, you will probably get cover worldwide without question as the product is pretty standard worldwide (baring specific language settings etc). Similarly, most laptops will pass under the waranty radar too. It is iPhones and Cellular iPads that really create the hassle. To be fair there is very little Apple can do about this and they make it very plain on their warranty website (check out the link above).
I have been using Apple for over 20 years now and always find that if you book an appointment in store (rather than just trying to call up) they will "normally" try and help you when they can - its one of the reasons I love them so much!!