"What powers does the Queen have?
The Queen has the right to rule: the people of Britain are not citizens, but subjects of the monarch. Most public servants must swear an oath of loyalty, or make an affirmation of their loyalty, to the crown.
Although the Queen is politically neutral, she has the right to be consulted and to "advise and warn" ministers. Otherwise her residual powers - the "royal prerogative" - are mostly exercised through the government of the day. These include the power to enact legislation, to award honours (on the advice of the prime minister), to sign treaties and to declare war.
But royal prerogative is the subject of controversy, because it confers on governments the power to make major decisions without recourse to parliament. When Edward Heath brought Britain into the EEC in 1972, parliament was not consulted until afterwards. Similarly, Margaret Thatcher used royal prerogative to go to war in the Falklands in 1982.
The Queen has two individual powers that could cause a political crisis if they were ever exercised. She may refuse a government's request to dissolve parliament and call an election, if she believes a government can legitimately be formed. She also has the right to choose the prime minister: a formality in the case of a clear majority, but potentially controversial after an inconclusive general election. This almost happened in February 1974, when Labour failed to win an overall majority but the Conservatives considered power-sharing with the Liberals."
(taken from here
Don't know about you, but I'd far rather be a citizen rather than a subject.