My cat, miaowing incessantly at 3am to be let out interrupts a long rest, especially if I lose the initiative check with my wife to be the one who has to let the demanding feline out.
On a more serious note, I did fight off an intruder once (in my serious rugby playing days) and chased him down the road, until the fact that it was January, snowing and I was barefoot, allowed him to outpace me. Dealing with the police report interrupted my long rest that night.
Oh, we’re talking D&D......the night hag in ToA was a pretty memorable interruption of a long rest, and it seriously screwed over my druid’s spell ability.
Then there was the rainy night in a shallow cave on a mountain pass, with an improved invisibility assassin, name of Mylekek, sneak attacking through the night...one of the scariest experiences I’ve had in the game.
Or, the long rest Fayleen, my bard, spent in Ireena’s bedroom to help her sleep, with Strahd appearing at the window. Long rest kicked resoundingly into touch that night!
The first and third didn’t involve an initiative check (which is my rule of thumb as well) but definitely killed off the long rest.