Here is the relevant passage from Plutarch:

Many rushed upon Alexander, for he was conspicuous by his buckler and by his helmet's crest, on either side of which was fixed a plume of wonderful size and p267 whiteness. But although a javelin pierced the joint of his breastplate, he was not wounded; 6738 and when Rhoesaces and Spithridates, two Persian commanders, made at him together, he avoided the one, and smote Rhoesaces, who wore a breastplate, with his spear; and when this weapon snapped in two with the blow, he took to his sword. 9 Then, while he was thus engaged with Rhoesaces, Spithridates rode up from one side, raised himself up on his horse, and with all his might came down with a barbarian battle-axe upon Alexander's head. 10 Alexander's crest was broken off, together with one of its plumes, and his helmet could barely and with difficulty resist the blow, so that the edge of the battle-axe touched the topmost hair of his head. 11 But while Spithridates was raising his arm again for another stroke, Cleitus, "Black Cleitus," got the start of him and ran him through the body with his spear. At the same time Rhoesaces also fell, smitten by Alexander's sword.

Alexander almost was killed by a battle axe. This was at the Battle of Granicus when he was facing a provincial Persian army. If Alexander had died that day, he would not have conquered the Persian Empire. Greek culture would not have spread nearly as wide as it did. It would have profoundly affected both the development of the East and West.