Prime Minister of the United Kingdom
Although the nominal head of state of the United Kingdom is the monarch, currently the Queen Elizabeth II, real power falls with the head of the government; Her Majesty's Prime Minister. Although the British Prime Minister is not officially the head of state in the same way that the American President is, they still wield many of the associated powers.
Unlike in the United States, the British parliament is not voted on separately from the Prime Minister. Officially, the Prime Minister is selected by the ruling monarch, and is expected to be someone who has the support of the British parliament. In practice, this means that the leader of the current majority party is made Prime Minister. For example, when the Labour Party won the most seats in the 1997 general election, the current leader of that party, Tony Blair became Prime Minister. When an election produces a hung parliament (rare under the British system), the monarch will offer the position to the leader of the largest party. If they are unable to form a government that has a majority support (either through a coalition or ruling as a minority), the monarch will offer it to the next largest party leader, and so on. The method of appointing the Prime Minister means that it is possible for a PM to be unelected by the populace; they only need to become leader of their party. Although this is uncommon, the current PM, Gordon Brown was appointed in this way. Despite intending to call an election, warnings of a narrow Conservative victory stayed his hand, and the plans for an early election were cancelled.
Current Prime Minister
Currently, Gordon Brown is the leader of the Labour Party, and thus Prime Minister of the United Kingdom. However, Gordon Brown's Labour party have yet to win a general election; he became Prime Minister as part of the victory won by the previous leader, Tony Blair, in 2005. In fact, opinion polls suggest that the Labour party is currently (2008) less popular than David Cameron's Conservative Party, though the gap in the polls is closing. Legally, Gordon Brown is obliged to hold such an election by 2010, baring special intervention as in World War One and World War Two.
Although officially the powers of the Prime Minister are quite vague, mainly to "form a government", a good deal of the selections officially made by the monarch are really made by the Prime Minister, including knighthoods and peerages. Recently, the Prime Minister has become more powerful within the government, and some have criticed the office as being a "British Presidency". This would be problem as it effectively means that the British head of state is not voted on by the people, but chosen by party. The incumbent Prime Minister, Gordon Brown, has proposed handing some powers back to Parliament, such as the power to declare war, reducing the overall power of the Prime Minister.