Mearlchan, one of the reasons these things are difficult is because law still isn’t settled in these areas. When you add international complications, things get even hairier.
The Berne Convention (named after the Swiss city) only provides the most meager of harmonization, basically saying that countries should respect the copyright of foreigners on the same basis as the copyright of their citizens. (hence the origin of the copyrighted work is irrelevant for the level of protection) If a state would only offer a minimal protection anyhow, that would not be a problem for the convention. Things are getting more interesting with the WIPO treaties such as TRIPS, which are going more in the direction of a world-wide harmonization.
For international cases such as the one you pose, you have to think in terms of action. Where would the copyright holder prosecute? Mostly people prosecute either in the state where the infringment takes place or where the plaintiff resides. If we assume the former, and we assume the place is Europe, the copyright holder should be able to get an injunction against the infringment and an award of damages (barring any particular exceptions, of course).
You can complicate this further by asking what the ‘place’ is where the infringment occurs: if you copy a work from a Japanese server to your private server space in Europe, but orchestrate it from your desk in the U.S., you could put a case for each of the three countries/areas as the locus delictus (?).
I can’t tell how it would play out with a U.S. or Japanese judge, since that depends on local International Private Law, possibly combined with local Copyright Law. However, I’d be surprised if U.S. law would without further ado allow private persons to copy copyrighted images to their computer. Some of the other posters seem to assume this, but I haven’t seen any references that support that opinion. AFAIK you’d still need permission in the U.S. except insofar a fair use exception would hold. I can’t see that here. (For my own reference see *).
One of the problems with legal GQ’s on copyright here on SDMB is that lots of posters ‘answer’ questions saying that things should be allowed. Such a moral stance may be interesting, but I doubt whether any judge would be convinced if you’d defend yourself refering to the opinion of the learned mr. X, well-known SDMB poster. 
Furthermore all this is just speaking generally. In copyright cases a lot depends on the specific facts, since there are lots of exceptions to the main rules.
So again this leads to the conclusion that if you want to know what is allowed and what is not in a specific case, you’ll have to consult a lawyer. I’m not your lawyer, and you’re not my client. And all the other standard disclaimers.
- See the EU Copyright Directive 2001/29/EC of of 22 May 2001, art. 5 for the ‘caching’ exception (also considerans 33).