Ah, the British Empire! Who here has not dreamed of a world in which the Union Jack still flies proudly over Suez and Bombay, New York and Honolulu? A world in which the medium of exchange is not Dollars or Euros (urgh!) but good old Pounds Sterling (240 d.)? A world in which fast food means greasy spoons or cod and chips wrapped in old newspaper? Where films means Ealing and cars means Austin, Bedford and Morris?
Possible reasons for the decline of the British Empire include:
Wikipedia has an article about the British Empire, if you're interested.
The Anglo-Dutch Empire by Flocculencio et al. The POD is that William of Orange had a son.
Monarchy World by Tony Jones. The POD is, among other things, the American Revolution being avoided.
The Two Georges by Richard Dreyfuss and Harry Turtledove, set in a world where there was no American Revolution.
The Warlord of the Air by Michael Moorcock (1971), the first volume of his Nomad of Time trilogy. One of the PODs is that there was no First World War. This novel is also famous for its widespread usage of airships.
The Peshawar Lancers by S.M. Stirling. After a series of comet impacts in 1878, the British government relocates to India, forming a New Empire from the ashes of the Old. By 2025, technology is still at the level of our world's early 20th century. However, the New Empire is far more Indian than British, and goes by the name “Angrezi Raj”.
Anti-Ice by Stephen Baxter.
The Gernsback RPG campaign setting from GURPS Alternate Earths. The Second World War never occured.
The Cornwallis RPG campaign setting from GURPS Alternate Earths 2. The American rebellion is put down.
As an historical epoch, the era of the British Empire was the pinnacle in the history of global politeness, snootiness, and tea consumption. As a political entity, it spanned half the globe and at all times of the day at least part of it received sunlight, which was diligently blocked out by wide-brimmed hats and the accompanying warmth disregarded in favour of well-starched formal clothing. The collapse of the British Empire was definitely not the fault of any British person.
An excellent rant: AH.com and the British Empire: A Rant