I have bought Apple HW in Switzerland, which I had AppleCare on in Denmark. US bought HW which I had fixed in Switzerland and in Denmark, and finally HW from the Phillippines, which I had fixed in Denmark as well.
The only issue I have experienced was with a Swiss service provider who had to be ordered by Apple to replace a US bought TimeCapsule. There supposedly is a difference in the WiFi component, and as he didn't have a US model, hence he couldn't replace like-for-like. I got a European model instead though. I was in the store when Apple talked to the guy over thephone, and the look on his face was priceless when he was ordered to accept the US TC and give me a new one. He stormed out and someone else had to finish the service call.