She's the ambassador of the UK. She has far more influence around the world than any PM will ever have, and does wonders for international relations (though usually within the commonwealth). She can get away with visiting countries that the PM couldn't, thus spreading British interest/influence and potentially strengthening bonds of alliance between the UK and other nations.
Plus the Royal Family is a massive tourist attraction and draws many people to the UK every year, far offsetting any cost to the taxpayer in terms of revenue gained by the country as a whole.
Additionally if we did end up in a state of dictatorship or a really crappy government that's seriously jeopardising the state of the UK, the Queen still possesses the power to dissolve Parliament, and the army is still the Queen's army. So theoretically (whether it would work in practice I don't know) she's a check against a potential rise of extremism and people who are really, really awful at running the country.
But please think before you make a post sounding so...critical. If you don't have the slightest clue about the interaction of the Monarch/Parliament then maybe ask about the role *without* stating that she's just a drain on resources?
[sub]Besides, we all know you're just jealous because we actually have history - it'd be pretty weird if the US had a monarch when you don't even have castles (made of stone - Disneyworld is plastic and doesn't count)[/sub[
