While the Royal family still has "powers", generally they act on status-quo for the large part. In reality, the Queen could refuse to sign a bill that goes through parliament, although it is highly unlikely to happen. If the Queen were to not sign a bill it would have to be something really stupid that managed to get through the House of Lords and the House of Commons. Say for example, they all go insane and declare they would like to sell off all of England to Germany...then she could reject it. Basically, she doesn't really even sign all the bills personally, but instead signs a general document saying that she has given Royal Assent to a list of pending bills that she has glanced over (this is announced in the parliament). In Canada, the representative of the Queen (the Governer General - Adrienne Clarkson) fulfills two important roles. Firstly, she represents Canada globally, and is usually travelling on tours to meet other Heads of State. Secondly, the really important role she does is disolve parliament come election time. She is also technically (I think) in command of the Armed Forces, being the highest ranking officer in Canada (but she doesn't give the orders to Generals).
Probably the most well known role for the Queen in England is that she is the head of the Church of England.
Hope this helps,
-Duncan