In 2014 holders of an Australian passport can visit 168 countries and territories visa-free or with visa on arrival
These are the countries which an Australian can visit without visa:
- South Africa
- United States
- Saint Kitts and Nevis
- Saint Lucia
- Saint Vincent and the Grenadines
- Antigua and Barbuda
- Costa Rica
- Dominican Republic
- El Salvador
- South Korea
All countries except: Russia, Ukraine, Belarus
Australians can visit a lot of other countries with visa on arrival, which can be done at the borders and for some countries can be applied easily online before arrival. Average costs of visas on arrival are USD 30.
Please refer to the Wikipedia article for the full list:
Neither Wikipedia nor this Quora answer must be treated as an official reference. Always check with the country embassy in Australia.