The Australian Parliamentary Library has a background note on hung parliaments [pdf warning]. The document notes that it refers to the House of Representatives in the Australian national parliament and not the Senate.

The upper house has had non-majoritarian representation for quite a while, largely because of the Australian Democrats or Greens having the balance of power. Interestingly the Senate used to be winner takes all. So if Labor won a state they got all six Senators and vice versa. Labor changed the voting mechanism to proportional voting in the hope of gaining more seats; ironically they have not had a majority since;

Since 1949, when the current proportional representation voting system commenced, governments have only had absolute majorities in the Senate for a total of 17 years (1951-56, 1959-62, 1975-81 and 2005-08)

The reason a hung parliament is important in the House of Representatives as this is where the executive is formed. Unlike the Washington system where the Executive (President) is elected directly, the Westminster system elects representatives to the House of Representatives where a majority will form 'government'. Or in other words through the majority of the house establish an Executive Cabinet that is recognized by the Governor-General who heads the Executive Council for the head of state; the Queen.

Despite Australia having a Washminster system which mixes a (Washington) written constitution and federal system with the Westminster system, it often relies on conventions or mos as the Romans called it which was existing constitutional practice;

The Commonwealth Constitution does not provide a mechanism for resolving a hung parliament. Rather, unwritten conventions work to resolve the situation. It has been noted that, if after an election no party emerges with an absolute majority in the House of Representatives, 'the incumbent Prime Minister, as the last person to hold the confidence of the House, has the right to remain in office and test his or her support on the floor of the House'

The deal that was wrung out by Gillard and the independents was that the latter would ensure supply. These are the money bills that keep government going and fund the policies of the executive. This has been a sticking point in the past in Australian politics as the Liberal Senate blocked supply on the Whitlam government and caused a constitutional crisis.

The minority Australian Democrats when they held the balance of power in the Senate usually ensured good governance through not blocking supply but it was obvious that holding up money bills was their major bargaining chip. Practice has also changed and rather than one big supply bill, there are numerous pieces of funding legislation which makes the Whitlam sacking unlikely in the future.

From the background note on hung parliaments [pdf warning]; the last one was during World War II. The Prime Minister at the beginning of the war was Robert Menzies. As the war progressed he lost support until during an election in 1940 he managed to stay in power through a minority government.

The last hung Parliament occurred as a result of the general election of 21 September 1940. At that time there were 75 seats in the House of Representatives, and after the election the ALP and the Coalition of the United Australia Party and the Country Party emerged with 36 seats each in the House, along with three independents.

The balance of power was held by two of the three independents in the House, Alexander Wilson and Arthur Coles, both of whom supported the incumbent Menzies Coalition Government and enabled it to remain in office.

The independents' support lasted until 3 October 1941 when they voted with the ALP Opposition in its motion to reduce the first item in the Budget of the now Fadden-led Coalition Government by a pound (dollar) - one of the traditional forms of no-confidence motion'.

With this Fadden resigned and Labor's John Curtin formed government with the support of the independents until the next election when Labor won a majority in their own right.

Another interesting tidbit from the background note on hung parliaments [pdf warning]; there was nearly a hung national parliament in 1961 during the long period of Liberal (conservative) dominance by the Coalition.

At that time [1961] there were 124 seats in the House of Representatives, and the ALP and the Coalition of the Liberal Party and the Country Party emerged with 62 seats each.

The two members for the NT and the ACT, however, were only permitted by law to vote in the House on certain matters relating to the NT and the ACT, and both of these members belonged to the ALP.

This meant that the Coalition was able to remain in office with a 62-60 majority, although this was reduced to 61-60 after providing the Speaker for the new Parliament.

Fascinating.