Airlines -- From Canada, Air Canada offers service to Nashville from Toronto; and Northwest, American, and Delta all offer flights from various Canadian cities to Nashville and Memphis.
From London, you can get to Nashville and Memphis on American, Delta, Northwest, TWA, and United, or, via connecting domestic flights, on British Airways.
From New Zealand and Australia, you can fly Air New Zealand or Qantas to Los Angeles, and then take a domestic flight onward to Nashville or Memphis. United also flies to Memphis from New Zealand and Australia.
KLM flies directly to Memphis from Amsterdam.
Immigration & Customs Clearance -- Visitors arriving by air, no matter what the port of entry, should cultivate patience and resignation before setting foot on U.S. soil. Getting through immigration control may take as long as 2 hours on some days, especially on summer weekends, so be sure to have this guidebook or something else to read. Add the time it takes to clear Customs, and you'll see that you should make a 2- to 3-hour allowance for delays when you plan your connections between international and domestic flights.
In contrast, for the traveler arriving by car or rail from Canada, the border-crossing formalities have been streamlined to the vanishing point. People traveling by air from Canada, Bermuda, and some places in the Caribbean can sometimes clear Customs and Immigration at the point of departure, which is much quicker.