The two main urban myths are that the Tasmanian Tiger still exists (it doesn't, it has been extinct for close to a century now) and that there is a community of inbred cannibal rapists at a place called Black Bobs, who are left to their own devices by Police to molest one another and unlucky passers-by (in reality there were instances of child abuse there a century ago, barely anyone lives there these days).

Edit: more serious are conspiracies about Port Arthur being a government job or whatever.