This is the only major region of Australia that is not yet a self governing state. At a Federal election (in 1998), the territory rejected a referendum that would have resulted in the area becoming another state. While it might not legally be a state, many Australian residents regard it as being just like a state.
The territory covers about 1/6th of Australia but has a low population. Most of the area is within the tropics so this is a hot region. The northern third receives very high rainfall during the cyclone season (summer) while the rest has a desert climate receiving rain at unpredictable intervals.
There are many areas here where walking is possible but are relatively unknown. One problem with the territory is that large areas of relatively natural land is under private ownership by both farmers and native aborigines. While some readily give permission to cross their lands others do not and sometimes permission varies from year to year. A general guide cannot recommend walks on private lands.
The most popular and reliable walking areas are those where there are national parks. The Macdonnell Ranges are located near Alice Springs and a long distance walking track has been constructed, the Larapinta Trail. This provides some excellent walking through a desert mountain range. For experienced walkers there is some good off-track walking in the Chewings Range - this is near the Larapinta Trail. Further north at Katherine Gorge, there are many walking tracks. Most are designed for one day walks, the two longer tracks are the Katherine River Wilderness Walk (3 days) and the Jatbula Trail (5 days).
In the far north, the Kakadu National Park is one of the best known reserves in Australia. The eastern half of the area is an aboriginal reserve in which you are not allowed to enter. The western half of the park has some excellent bushwalking country and there are some fine walks of up to 5 days in length. Permits are required and are not readily given out so you must make arrangements well in advance if you want to walk in Kakadu. Restrictions apply because many aborigines follow a traditional lifestyle in the park and a strict permit system reduces conflicts and unexpected contact.
To get permission to walk in Kakadu, you must send in a map with your detailed route. This is often rejected if your route approaches a sacred or protected aboriginal site. They will not give you a list of sites to avoid, so obtaining permission from afar is a hit or miss affair. Practically, you need local knowledge to know where you can go and this makes it more difficult for visitors to obtain a permit. Many bushwalkers employ local commercial guides for walks in Kakadu as they have the required knowledge and this is a practical, although expensive, alternative.
Litchfield National Park is popular with local walkers and provides trips from 2 to 5 days in length. Located just south of Darwin, permits are easier to obtain than for Kakadu. This writer has not yet visited this park so I cannot yet recommend any particular walk.