One of the most pivotal moments in one of my games came when two NPCs were fighting - one on the same side as the party, one against them. The 'ally' was Shaaladel, an elf revolutionary pretty loathed by the PCs for being an a-hole, but he was at least helping. The 'enemy' was Marius, a human knight responsible for murdering the parents of Rhuarc, one of the PCs.
Well, Marius failed a save to a PC's hold person spell. Shaaladel was right over him, sword in hand. Rhuarc shouted for Shaaladel to coup Marius. Shaaladel didn't want to bother wasting his full turn to coup someone who was already down when there was more glory to be found by fighting other enemies, so he scoffed and just made a single swipe down at Marius, then kept moving.
Well, that swipe was a natural 1.
Marius lived, broke out of the hold person, and escaped under cover of his guards.
This turned the fate of basically the whole campaign setting, because the PCs refused to cooperate any further with Shaaladel, which meant his elvish revolutionaries sought out a new alliance with the next most powerful force, one led by an orc warlord named Coaltongue. And that is how the War of the Burning Sky adventure path's backstory came to be. Because an arrogant elf figured he couldn't miss a sure thing.