In Australia we effectively have a two party system with a twist - a third party. Parties can be classified into three broad categories (Note that this may differ for other countries). A majority party is a party that can reasonably hope to gain a majority in the House of Representatives after an election (In Australia government is formed by the party holding the support of the House of Representatives). A major party is a party that can hope to gain the confidence of the House with the support of another party. Finally, a minor party is a party that cannot reasonably expect to gain the confidence of the House.
Australia has one majority party, one major party and a number of minor parties. The majority party is the Australian Labor Party (who, for some reason, can't spell labour like everyone else here). The major party is the Liberal Party, who can always count on the support of one of the minor parties, the National Party. It is exceedingly rare for anyone who is not a member of one of these three parties to gain a seat in the House of Representatives, so government is always formed by Labor or a Liberal/National coalition - effectively a two party system.
It is notable that there have been a couple of occasions when the Liberal Party has been able to form government without the support of the National Party and therefore without sharing the Cabinet with them but that have always chosen not to, as they will certainly need National support in future elections.
Although the National Party can influence the democratic process their influence is not very significant because they predictably vote with the Liberals. In recent years the two party system has started to crack with occasional independents and minor party (other than National) candidates elected to the House of Representatives. Also, due to the voting system used, the Senate has a higher number of parties represented. Traditionally, the Senate was not considered to have a say in the party forming government. This all changed, though, after the Dismissal, when the Senate forced the Labor Party out of government by refusing to pass Supply, which is a crucial part of the Budget.