mine all fall into the mildly annoying/amusing category

We lived in a unit on the 6th floor and the old duck upstairs would randomly and regularly move her piano across the floor at 3 and 4am and proceed to play it and sing along.

Our old next door neighbours here were the loveliest people....except for their obsession with the weather. We live in the desert. On a hill. In the wet last year dad (who works for BOM) was convinced that there would be flooding. I spent a weekend highly entertained by the ant like activity out the front as they filled and placed sandbags.
Then in the fire season (like 9 months of the year) I heard what sounded like rain and I looked outside. It was them hosing our roof - with their own personal fire trailer that they had filled with the pool water from their rental. lol The owners are friends with ours and nearly had kittens as renters don't pay for water here, even though it is hideously expensive. They were protecting us from fire (there was a large blaze a few kms away). Two days later the mountain in front of our house went up, and they came and knocked on my door afterwards and wondered when that had happened....they had been home the whole time.

Then there were our previous neighbours across the road. Supplying drugs. Until they realised that a copper lived here and lots of cops visited, and all of a sudden all the visitors stopped and they went out. A lot.