You may also be charged GST or VAT, however, Australian customs do not charge GST on personal goods valued under A$1000. My experience is that items just over A$1000 are often not charged GST. I advise that you not rely on avoiding being charged GST and factor in paying GST and duty on items valued over A$1000.
The GST limit applies only to the cost of item. For example, if an item cost US$650 with US$200 shipping then it would still be under the A$1000 limit even if the shipping made the total cost more than A$1000 at the current exchange rate (this is assuming an exchange rate of 70c).
In regards VAT or duty charges for countries other than Australia you will need to contact your local authorities. The VAT/GST thresholds for some countries are listed below. Take care using this data as it changes all the time and you are best to always check with your local customs authorities.
Australia • A$1000
New Zealand • NZ$220
Singapore • S$400
United Kingdom • £18
EU • €10 to €22