This is probably something really obvious for the most common, but I’m curious as to what it is.
For the least reported death, I’d imagine there would be multiple things where only one person has ever reportedly died from it. This doesn’t include murders where the thing that was used to kill the person was so unique that only have they been recorded as having died from it, if such a thing has happend.
You’re talking about the most common cause of untimely death, I assume? (otherwise, it’s probably ‘natural causes’ (i.e. old age), isn’t it?)
There are going to be a lot of deaths which only one person has ever suffered that particular kind, it depends how specific you’re going to allow it to be; i.e.:
“by an animal”: lots
“by an elephant” : not so many
“by being sat on by an elephant”: even less
“bby being sat on by an elephant named Stinky Jim”: not many, possibly zero
I can’t quote chapter and verse (tho’ perhaps others can) but my sister works in the UK’s National Health Service and apparently - when the chips are down - the primary cause of death is respiritory failure - which can occur for a wide variety of reasons, of course.
Untimely, yes.
Scrap my least question, as it has too many variables to answer properly.
I’d guess auto-erotic asphixiation. (I miss Upright Citizens Brigade…)
Gotta be Chuckles the Clown being squashed by an elephant while dressed as a peanut in a parade.
Ranch house defenestration.
Most common: cardio/pulmonary arrest.
Least common: Being eaten by a swarm of flying sharks.
The least common identifed accident death in the US in 2000 was a transportation death while an occupant of a street car - 1.
If we’re going to be realistic, and talk about real people dying of real diseases, I’d say that the WHO’s Internation Classification of Diseases (ICD) code 050 (smallpox) would be in the running for least reported cause of death.
The last reported case was 27 years ago, in Somalia in 1977. In fact, the code for smallpox has been dropped from the latest version (ICD-10).
I recall reading that only one person has ever been killed by being struck by a piece of an artificial satellite falling from its orbit.
A few years back, a zookeeper died while giving an elephant an enema. Got buried in Elephant do-do, and suffocated.
I bet the WHO doesn’t have a category for that!
Tris
I haven’t heard of anyone being killed that way. Any details?
And I don’t think anyone is known to have died by being struck by a meteorite either, although I could be wrong about that.
Snopes says: False.
According to the Guinness Book of Records, the leading cause of death in the industrialized world is arteriosclerosis (thickening of the arterial wall), which underlies much coronary and cerebrovascular disease.
Ah, the ICD codes. Of course, there are ICD codes listed for a great many neat things, like Injury While Passenger In Space Vehicle and Injury Incident, Military, Involving Lasers.
I wouldn’t go so far as to say that would be the source of a definitive answer, because as far as I can tell, there’s no ICD code for “decapitation.” I think you’d have to qualify that as “open wound, head/neck, w/ complication.” 
This interesting review of space debris that has fallen worldwide is unaware of any such death.
Well, I am not going to make my pal take down his poster. Damn that Snopes, anyway!
Tris
Can’t all deaths be classified as heart failure? The heart’s beating, you’re alive. It’s not, you’re dead. What induces the heart failure is another matter…
OK, I know that you could technically be alive with no pulse, but not for very long.
How I love to nitpick. 
I saw a documentary about a guy waiting for a heart transplant who was temporarily given an artificial heart that was little more than a small turbine pump - he had no pulse, IIRC, he said that he was acutely aware of his own lack of pulse and could hear/feel the ‘whine’ of the turbine instead.
It appear my memory is wrong. I found several references that corroborate the one Walloon linked to in saying no one has ever been killed by space debris.