Alex's answer gives a great explanation of the current political landscape in the UK and explains how the referendum came about at this particularly time. However, there are broader reasons why the UK would seek to leave the European Union while other countries do not.
First, the UK has never been as well integrated or invested in the EU as other nations. It was not among the founding members. Also, it often excepts itself from various EU policies whenever it can; a prime example of this is the fact the UK still uses the pound and did not adopt the Euro.
Secondly, though the World Wars may have brought an end to the British Empire, the UK still maintained a considerable amount of its economic, political, and military might. It's in a position of strength so being independent is more feasible.
Lastly, being geographically isolated, the people in the UK generally don't have the same cultural ties as many other parts of Europe. In many EU nations, national boundaries are kind of blurry because of cultural similarities.