Which aircraft in history have shot themselves down?

i guess quite a few, hit by shrapnel from their own bombing run.

In training scenario's or actual combat sorties?? the first subject would be to numerous to mention here, the second if documented through actual combat action reports is dependent upon what theater of operations you are referring to.

The F-4 Phantom II did indeed receive catastrophic results in an air-to-air engagement when the Sidewinder missile it was carrying detonated at launch over North Vietnam in 1967

F-104 Starfighter chased down his own bullets and if you count flying through your own rocket debris, an A-4E in VietNam. He fired the rocket pack and instead of one pod firing, all 3 fired at the same time. They ran together in front of the airplane, exploded and he flew through the debris. The engine lasted long enough for him to stagger back to the boat where he executed a controlled ejection. Scratch one A-4E.

If fact it happened a lot in WWI, that was why Fokker developed the synchronized machine gun.

But maybe you don't consider shooting your own prop off as gunning your self down.

So I would have to vote that it was the Spad.