I must admit that I haven' t experienced many problems of that sort with my neighbors. In my previous living place, the nuisance which was annoying me the most often was my neighbor's dog barking. I could't focus on doing anything. I lived in a block of flat so this type of disturbance can be very irritating, as well as for example drilling in the walls at 7 am. Next quite annoying thing was toddling the same neighbour's son. I like kids but his early (usually round 5 am.) pattering forced me many times to start my day sometimes before the sun.
In my neighborhood there is many pathological people and families, usually alcohol addicts. Those drinkers have in manner to accost any passer-by and demand him for money.
Many times I witnessed an act of family violence of my block-mates, my best mates were victims. Those extreme situations often were ended by police intervention and just warning.
I must confess that many times I was the troublemaker warned by neighbor's from below for too loud guitar-playing. They were knocking in the heater using hammer, which was clearly heard in my flat. Sometimes they visited me in person, and warn.
Currently I live also in a block of flats, but on the last, 4th floor. Luckily I live in peace and harmony with my neighbor's, except a mentally ill old lady from below. Sometimes she screams very early in the morning. Everyday she cleans whole staircase, and from time to time she leaves her flat door opened, but she is very gently and polite.