In a
parliamentary system, where
government is formed by the party which gains the largest number of seats in one
house, it sometimes occurs that no one party obtains an
absolute majority. It is therefore necessary for the larger parties to attempt to woo smaller parties and/or
independents in order that they might officially support their claim to office.
A hung parliament occurs when there is no way for any party to form government, either mathematically or due to a failure to reach compromise. In this instance the parliament would usually be dissolved and a new election called. In most such systems (many of which are based on the Westminster system) there is an executive, such as a Governor or President, who must approve the formation of government. In many cases this person's role is symbolic.
Minority governments are not as common as might be supposed in the case of assemblies elected using a system of proportional representation. Israel's Knesset is a prime example of this and it is almost always the case that no one party wins sufficient seats to be able to govern on its own. However, since the vote is so widely distributed, Israeli parties are forced to form coalition governments rather than minority governments. The distinction is that in a coalition, both parties hold cabinet or executive positions, usually in proportion to the amount of Members of Parliament each has.
Of course, there is such a thing as a minority coalition government, an example being the current government of Norway which hasn't had a majority government since before World War II. This has led to the resignation of several governments.1
Victoria, Australia, currently has a minority government. In the State election held in 1999, Steve Bracks' ALP won 41 (of 87) seats whilst Jeff Kennett's Liberals managed 43. However, three independent MPs had also been elected and despite having won a smaller proportion of the vote, Labor managed to successfully negotiate its way into power.
Large parties usually strongly dislike having to form minority governments as they must compromise their agenda to some extent or risk losing power. Small parties and independents want to make the most of their time, which they know will not last long, and are therefore not able to be bought off easily.
See also
balance of power
1. Thanks to Sverre for this info.