Another difficulty not mentioned so far is that in an emergency planes can and will land anywhere including military airfields. Hell, once a civilian plane landed at Kitsap of all places (it was not allowed to take off after). Now, of course most US military bases are on US soil but there are foreign ones and I have no idea whose law applies should your plane land at Ramstein Air Base for example. It’s a mess based on my readings.
All the resources in @kiltannen’s Answer will allow you to see historical flight paths between airports.
What you then need to do is eliminate all city pairs where a routing has had a US airfield as the nearest suitable landing point at any time. You can use gcmap.com to overlay direct paths and airports.
For example, you would not be able to fly from Eastern Australia or New Zealand to Japan because at some point, the nearest airport is Guam or other US territories.
There are a few options for you to look into:
Flight Stats provides comprehensive flight information for all flights originating in the United States and also fairly comprehensive coverage for overseas flights in Europe. For other countries, the data you receive is hit or miss.
The content it provides (on US flights) is comprehensive. You can see the flight path on a variety of maps, all powered by Google Maps.
Flight View offers much of the same information as Flightstats above. You get a live map (although not as pretty as Flightstats) time and delay information, and more. The one area where Flightview really shines is mobile apps. They offer free mobile flight tracking apps for iPhone, Android, Blackberry and other platforms.
Flight Wise Might be the best as it is geared more towards the technical information about a flight. And this may allow you to work out the potential for diversion into US and whether there is a flyover of US airspace.
There are quite a few other tracking sites, but these seem to be pretty popular for data about US flights, which I think is what you are more focused on right?
Credit:stackoverflow.com‘