I am really impressed by these answers. A lot of you seem to have thought of this already and have a firm decision. I don't know whether I am surpised that no-one has gone for My Way except for one person who has gone for an alternative (possibly an ironic, post-modern) version. Perhaps that is because CBF members are just too interesting - including one who is so "interesting" that he might consider getting psychiatric help for the condition.
I have never really considered it; perhaps I should. I am not sure how to start this. Perhaps I should follow Peter Seller's lead - who specified Glenn Miller's "In the Mood" apparently because he hated it so much that in having it played after his death he could share a final joke with his family and friends. If I did this I should surely pick Sinatra's "My Way" which I totally detest. Or since I am determined to be cremated perhaps I could go with J. L. Lewis' "Great Balls of Fire" - but that might be a bit coarse, not to mention egotistical. I might choose Bristol Rover's theme song, for no other reason than it would irritate my brother who is a Bristol City fan. But perhaps that song, written in prison by a man convicted of murder, and which may - possibly - be about that man killing his wife, wouldn't be the most decorous. In equally sombre mood it might be "St. James Infirmary" (the Snooks Eaglin version) that Hilary says is the most miserable song ever written and which I am absolutely forbidden to sing in a public house ever again. I toyed with the idea of making it Cab Callaway's "I'll Be Glad When You're Dead You Rascal You" - but since I hope to die at an improbably old age my "rascal" would likely have been long dead.
So, in pondering this important issue, I'll take your replies into consideration ... except for one - get help man whilst there is still time.