First off, A HUGE CAVEAT: do not ever let yourself, your journeys, or your imagination be limited to existing "official" trails and routes!
The second thing is that "long distance" is a highly subjective term. My personal criteria is that a "long distance" journey should last at least a few weeks (three probably being about the minimum), but then what one person can cover in a week might take another person three weeks, and when it comes to multi-use trails, whether you are walking or cycling can obviously makes a huge difference in the trip duration. And what about, if you take my caveat to heart and want to string together a bunch of shorter trails into a long journey? This is probably how many longer distance trails got their start, and something I very much encourage you to do. So the second caveat is that this list is highly subjective and far from comprehensive. That said, if you know of a route or trail that you think should be on this list, please email me and tell me about it.
And no, the map isn't upside down!
Australian Alps Walking Track This trail runs from near Melbourne to near Canberra along the spine of the eastern mountains, and comes into close enough proximity of the three highest mountains in Australia that you can "climb" them all in one day (only the second highest, Mt Townsend, requires so much as even minor scambling near the top). The mountains of this continent are geologically ancient and worn down, but the landscape is full of wonders nonetheless.
Australia has some great long distance hiking trails, through a diversity of landscapes. For info on these, as well as a some shorter trails, follow this bushwalking link on John Chapman's website.
Te Araroa - The Long Pathway - is a 3000-km trail stretching from Cape Reinga in the North of New Zealand to Bluff in the South.
There do not appear to be any "official" long distance routes in Africa. This is hardly surprising since Africans undoubtedly have other priorities, being as Africa is the poorest continent on earth (one which is still trying to recover from extensive exploitation by european colonialism). According to the IBIKE website, walking is the major form of transportation here. A few non-africans have explored the continent on foot - watch the video below - and certainly quite a few have done so by bike. Whether or not this is another form of colonialism is of course open for debate and something that every world traveller can only answer for themselves.
A super ambitious project to create a 9700 km trail running the length of Chile. The official site is in spanish. A bit of english language info is available at this site. The trail was original slated for completion in 2010, but the trail is still very far from complete. Don't let that stop you though!
The Nuxalk-Carrier Grease Trail (Alexander MacKenzie Trail) - British Columbia
There isn't really a website for this 350+ km historical trail between the Fraser River near Quesnel and the Rainbow Ranges in Tweedsmuir Park, but check out this site for a bit of info about both the First Nations' and european history of the trail.
The best source of info for actually hiking the Nuxalk-Carrier Grease Trail (Alexander MacKenzie Trail) is John Woodworth and Halle Flygare's pocket guide In the Steps of Alexander Mackenzie. There are still a few copies of the 2nd edition (published in 1987 - but still very useful) available from John Morton at the Kopas Store in Bella Coola. Email him at jmorton(at)belco.bc.ca (replace the at with @) or phone 250-799-5553.