Current polls indicate that there is a high possibility that the general election of 2010 in the United Kingdom will result in a hung parliament. The polls, both independent and those conducted on behalf of political parties, predict that the Conservatives will win only 40% of constituencies, 10% short of that needed for a majority government.
In the UK political system, each of the constituencies, whose number rose from 646 for the previous election to 650 for the May 6th poll,  is represented by one Member of the House of Commons elected under a first-past-the-post-system. Under normal circumstances this usually favours one party, which if it wins over half of the seats, will hold a majority government.
With a working majority the ruling party can implement its legislative programme without the co-operation of opposition parties. However with small majorities party whips have to struggle to ensure that their backbenchers remain healthy, turn up for and actually vote in favour of their party's legislation; to prevent parliamentary rebellions the party leadership may need to moderate their policies or make concessions to factions within their own party.
If a party fails to gain the 326 or more seats needed for an outright majority, then the incumbent party is the first to be given the chance to attempt to form a coalition government by negotiating with the smaller parties.
In a coalition government the MPs of the junior partner are in effect taking the party whip of the senior party. Depending on how much their aid is needed, the junior party may gain in return some of the Minor Offices of State and some junior ministerships. The senior party may also adopt some parts of the junior party's manifesto or to abandon parts of its own. The stability of such coalitions will depend on how closely aligned the parties are politically, for example the Unionist parties and the Conservatives are traditional allies.
In normal circumstances the 'fringe' parties such as The Green Party, UKIP and the controversial BNP, would be of no consequence. Unlike the elections for the members of the European Parliament, which uses proportional representation, the support for these parties, though significant, is too widely dispersed to have an impact. However, due to the disaffection with the main stream parties caused by the Parliamentary expenses scandal, there is a possibility that one or two seats may fall to the minor parties.
As the third party in British politics, the Liberal Democrats would be the main target of negotiation, and their leader Nick Clegg has been described as a potential kingmaker, with electoral reform—especially the introduction of proportional representation—being the traditional price for their support. However, after Labour Party reneged on their 1997 promise of electoral reform, they are unlikely to enter formally into a coalition with Liberal Democrats.
If the incumbent party is unable to negotiate a majority, then the party with the greatest number of seats is given the chance to form a government; this may be the incumbent party itself. If not, it will likewise attempt to negotiate with the smaller parties in order to gain a majority. It is only when this has failed that the party with the most seats may opt to govern as a minority government.
A minority government would be constrained as to its ability to legislate. More specifically, it would not be able to enact legislation without either the formal support, usually with a quid pro quo, of the opposition parties. The minority government could also propose legislation that is attractive enough to tempt opposition backbenchers to defy their own whips and support the government. Although the situation may seem unattractive to the political parties, the inability of any party to make major changes without a consensus across the house makes it attractive to some voters.
However, the instability and unpredictability of a minority government would be of concern to financiers who warn of further financial and economic troubles if such a regime came into power. Nick Clegg, the Liberal Democrat leader, suspects that it could to lead to social unrest like that in Greece in recent days. History has shown that the ruling party would find it impossible to work as a minority government, leading to an early general election.
Although such calculations have not been part of Westminster politics since 1974, they have been prevalent in the devolved Scottish and Welsh legislatures. The Scottish Liberal Democrats formed a coalition with Labour in the first two sessions of the Scottish Parliament, and the Welsh Liberal Democrats were in coalition with Labour in the Welsh Assembly from 2001 to 2003.  
Either way, whether the election results in a coalition or minority government, the possibility of the first hung parliament since the general election of February 1974 will be on the mind of at least the leaders of the political parties, if not the voters themselves.

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Current polls show high probability of hung parliament in 2010 UK general election