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One World Distances has a list of some direct flights that exist (or did exist at that time it was done). These are flights with a single flight number. They may go via several airports. Some even require a change of aircraft, like MIA-NRT on AA, but they are a single flight number, which is the important thing.
Flights between destinations are being reduced every day, with current world problems, so you need to check with the airline web sites.
[This message has been edited by Mwenenzi (edited 04-24-2003).]