Does the British Empire still exist? In a word, no.

In a strictly legalistic and narrow sense, of course, it technically does, because Britain retains control over a number of territories, such as Anguilla, Montserrat, Ascension, the Caymen Islands and the Virgin Islands.

However, ask yourself- would you call this an empire? There is no sense of command or power that is associated with the notion of empire. If it were so, then where do we draw the line? Every country which owns a small rock that is removed from its immediate vicinity or historical border would have to be considered an 'empire'. I think it is an important point that any typical person in the street would in no way be conscious that Britain is currently an empire and that it is considered a relic of the past.

With regard to the Queen's title: she is Head of State of some 17 countries around the world, as well as Head of the Commonwealth. However, when she visits Canada, for example, she does not visit as Queen of Britain; she is Queen of Canada. She is Queen of each territory, not of Britain alone. Furthermore, in none of those countries does she hold absolute power. As in Britain, she cannot act elsewhere without the advice of the elected government. She does not even appoint her Governor-Generals. Similarly, as Colonel-in-Chief of overseas armies, she has no power.

With regard to the Commonwealth, it is even more technical. The title of Head of the Commonwealth is vested in her person, not in her Crown- i.e., it is not inheritable by Charles, or whoever next is monarch of Britain. When she dies or abdicates, the Commonwealth will get together and decide who will be Head next. It may be they decide to rotate it among the Commonwealth countries; it may be they decide to give it Charles. It is a very common British assumption to fuse the Crown with the Monarch, but in other Commonwealth countries they do not make the same assumption.

Finally, the honours system still refers to Empire(OBE, MBE, etc.). However, they are titles and in name only. Changing their names would create unnecessary difficulties. Other titles are no longer awarded- for example, the ones referring to India ceased in 1947 when India became independent. Australia, Canada and New Zealand have the right to their own awards, many of which have the same names and are held in the same status as the British awards. They are awarded, of course, by the Queen of Australia, Canada and New Zealand respectively, not by the Queen of Britain.

EDIT: To further clarify my position on what I mean by the British Empire still exists in a limited, technical sense- Britain still has overseas territories, or dependencies, which it acquired via conquest or colonisation, in which Britain still has responsibility for external relations, whose citizens are 'British Overseas citizens' but all have the right to British citizenship, and where the Queen remains sovereign. This of course is an extremely limited definition but it seems reasonable to me that it is accurate in the light of what I consider to previously have been the British Empire.

Therein lies the crux. The main issue in arguing such a question is how you define 'the British Empire'. It is not even a matter of agreement that there was one- many people argue that there were two, or even three, which overlapped. Some argue whether it existed at all. So before one argues about the existence of the British Empire, ask yourself- what do I mean by British Empire?