I was a passenger on a flight (BA155 LHR-CAI 777) approximately 10 years ago that had the misfortune to have a passenger die in-flight.
We were flying over what used to be Yugoslavia when a 'is there a doctor onboard?' announcement was made. Very shortly thereafter the cabin crew were instructed to immediately suspend the meal service and clear away all passenger's meal trays, etc.
We made a descent into and landed at ATH. I was sat in 10D (CW), the deceased was in Y, so I never saw anything first hand - but we were subsequently advised by the captain that a passenger had sadly passed away and been removed from the aircraft.
We resumed our journey approximately two hours later. All handled very professionally by BA's crew.
A sobering experience though - I guess it could happen to any of us at any time.