I've known of two people in my circle of acquaintances who have died on airplanes from non-crash situations.
One was in his late 40s; he suffered an aneurysm mid-flight and passed away. Also, a 70-something family member of a close friend died on a flight about 20 years ago. She had just gotten on the plane and taken her seat. Before the plane pushed back her seatmate noticed that she wasn't breathing and summoned an FA. She had expired of natural causes.
I also knew a lady who was a passenger on American 77 that crashed into the Pentagon (she was a year behind me in college); also, a business partner of a client of mine died in the Delta 191 disaster in 1985.
This is a lot more common than you think; although I can only remember three times when I was on a flight when the FA got on the horn and asked whether a doctor was on board.