Recent experience from Nepal suggests you should, and the government's Smartraveller website (www.smartraveller.gov.au) provides a convenient way of doing so.
In the aftermath of the first earthquake to strike Nepal on April 25, it emerged that the Australian government had no idea how many Australians were in Nepal, who or where they might be or how to contact them.
Providing assistance to any Australians who might be injured or stranded becomes problematic in such circumstances, especially when set against the backdrop of a natural disaster that has taken thousands of lives.
According to Michele Eckersley of World Expeditions, which had hundreds of clients in Nepal at the time, it was left to them to contact the Australian government to provide a list of clients, their locations and state of health.
Fortunately all were safe, but for travellers making their own arrangements, the picture might have been different, and Australian government assistance might have been slow in coming to anyone in need.
The "Register your travel plans" link appears on the Smartraveller homepage, it takes just a few minutes to complete and gives the Department of Foreign Affairs and Trade all the information they need to track you down in an emergency.
Completing this information should be a priority for every traveller, especially if it involves the Third World.