One hand gesture that Americans should avoid making in Australia is a peace sign, or V-shape made with the index and middle fingers, particularly with the back of the hand facing outward. This gesture is the equivalent of a middle finger in most English-speaking nations, including England, Australia, Scotland, Ireland and New Zealand.
U.S. President George H.W. Bush caused a minor kerfuffle when he made this gesture during an official visit to Australia in 1992 during his presidency. Though the peace or "victory" sign, with the palm facing outward, isn't necessarily offensive to all Aussies, it's best to err on the side of caution.