I will be in Korea for 5 months, I'm about to buy an iPad 2 there and I'll be back in London or France in September. I would like to know if my warranty will be valid in England or in France in case something happens because there are no Apple Stores in Korea, but only retailers.
Yes. But with a cost.
From Apple's iPad warranty docs:
If you seek service in a country that is not the country of original purchase, you will comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges. Where international service is available, Apple may repair or exchange defective products and parts with comparable products and parts that comply with local standards. In accordance with applicable law, Apple may require that you furnish proof of purchase details and/or comply with registration requirements before receiving warranty service. Resources with more details on this and other matters on obtaining warranty service are described below.
UPDATE: Even in 2017, the situation is still the same and has not changed. This screen capture is from the Apple website dated 2017-08-04:
After leaving a comment on @anthonyg's answer, I realised this question is 2 years old. Exactly two years ago, I was living in Thailand but before moving there I purchased two iphones (one each for my wife and me).
The long of it appears in anthonyg's question, the short of it was that both developed warranty issues and whilst my MacBook Pro was in getting something fixed under warranty, they (the authorised apple reseller/repairer) refused to take our phones because they were purchased in Australia. I called apple whilst I was standing in the store and they backed the repairer. They would not honour the warranty for the iPhones in Thailand even though the phones were well within the warranty period.
From my experience, this will be fine. Apple doesn't seem to be fussy about warranty cards and the like, they just take the device, look at the serial number, and that tells when it was bought. I've had no problems with getting devices bought in the US serviced in Thailand, as long as it's within the warranty period. This has never involved any extra cost.
Unlike some companies, Apple seems to accept the reality that these days, people are very mobile, moving from one country to another. This is different to, for example, cameras, where warranties can be quite restrictive.