This article describes routes between countries that avoid transit in the United States, since the documentation requirements to transit in the US can be onerous. It may be preferable to select itineraries that avoid the United States altogether. However finding these flights is not always easy: the United States serves as a hub for many airlines; most online travel services lack an option to avoid a country; in many cases the smaller companies and chartered flights are harder to find.
Many travellers continue to transit through the US; not all travellers will consider it important to avoid it. However, you may wish to avoid transit in US airports because:
The United States does not allow sterile transit, which means that even if you have an immediate connecting flight, you have to pass through Customs and Immigration. This is time-consuming and tedious (4 hours or more is recommended to be safe), and all travellers transiting in the USA using either a transit visa or the Visa Waiver Program will be photographed and fingerprinted.
Anyone arriving into the United States or one of its territories (like Puerto Rico) and not covered by the Visa Waiver Program requires at least a C1 transit visa to transit the airport. This can be expensive and time-consuming to obtain, and you can be denied the visa: the requirements are the same as the full B-2 tourist visa. If you arrive without this visa and aren't eligible for a waiver, even for a fuel stop or transit, you will be sent home and recorded as having been denied entry to the US.
You have previously been denied entry to the US or overstayed in the US, and have been advised that entry may be refused in future. Transit entry is as likely to be refused as any other entry, it will almost certainly be easier to avoid risking it.
Note that all of these activities now require either a Visa Waiver or C1 transit visa:
transferring to another flight;
just stopping and not disembarking from the plane; and
Note that sometimes these minor stops are not even clearly marked on preliminary itineraries for long haul flights. If you have reason to avoid the US, ask that the itinerary be double and triple checked for transit and fuel stops in the US (including Hawaii).
Traveling from Europe or Asia via Canada allows reaching a number of Caribbean and South American destinations with no direct services. This is also useful for flying around the world without entering the United States. There are numerous services from European cities to Montreal and Toronto, and Vancouver and Toronto have non-stop services to Seoul, Tokyo and Hong Kong. However, some Toronto to Hong Kong flights refuel in Anchorage, Alaska.
Santiago de Chile and Sao Paulo can be reached from Sydney via Auckland. These flights are substantially shorter than trips via North America, but are less frequent and can be more expensive. Book well in advance. Onward flights to the rest of South America and up to Mexico are available from Sao Paulo.
Trans-Pacific travel avoiding the US can be difficult due to the use of Honolulu as a refueling stop. As Hawaii is a US state, a stop in Honolulu is a US transit. Insist on having your itineraries checked for this fuel stop, as sometimes it is not advertised. The most common other points of transit (and unfortunately the ones on the cheapest flights) are Los Angeles and San Francisco.
There are currently no non-stop flights to Canada from Australia or New Zealand. Flights advertised as Sydney or Melbourne to Vancouver direct have a fuel stop in Honolulu. You will need to book flights to Canada via the major Asian cities such as Singapore, Bangkok and Hong Kong. Even then, check that there is no transit or fuel stops on the US West Coast.