I voted Potato because it seemed an interesting option, and none of my current neighbours annoy me. But I'm in a middle storey flat in a Victorian terrace, so have been able to hear noise when I did have bad neighbours.
The people downstairs never give me any trouble. But living there before them was a couple who frequently rowed. He was really cruel to her, and I had to call the cops on him one night when I heard him beating her up. He came upstairs the next morning to give me some shit, demanding to know why I thought he was a dickhead. I told him if he didn't want people thinking he was a dickhead, he should treat his girlfriend like a human being. She got pregnant shortly after, and I don't know if he still hit her, though I heard him shouting some downright vile things at her quite regularly. Stuff like "GET YOUR FAT ARSE IN HERE!" and her crying. Like someone else said upthread about her neighbours though, he usually played loud music to drown out the noise of their rows. I bumped into her one day in the shop and asked her if everything was all right as I'd heard raised voices. She defended him immediately, saying she was just getting emotional from hormones/sickness, and it freaked him out as he was a "big tough guy" who couldn't understand why everyone else couldn't put on a front. I thought, well he can't be that tough if he's so freaked out by his missus being upset/ill that he bullies her instead of giving her a cuddle and making her a cup of tea, but I tried to make light of it by saying "Bloody men! I bet if it was him that had to get pregnant he'd be singing a different tune!" I knew if I made a big thing of it she'd clam up and never tell anyone, but I did tell her if ever she was stressed or needed a girlie chat, she could always come up to my flat for a cup of tea. They moved away shortly after and she left me a note with her phone number on it in case she got any post. Some letters did arrive and I texted her to let her know, but she never got back to me. In the back of my mind, I've never been able to stop wondering how she is, and hoping she somehow found the strength to leave the bastard.
In the top flat about three or four years ago, there was a Muslim couple with their newborn baby, who tried to guilt me into converting to Islam. The wife had converted from Judaism and was trying to convince me that Islam was the only right, moral way to live. They'd invited me up to their flat for a cup of tea but I quickly made my excuses as soon as I realised they had a hidden agenda! Before them, there was a really nice guy called Chris who lived there with his beautiful black cat, Coco. He let me borrow her to sort out a mouse problem I was having at the time. A Polish couple live there now, and I've never had any trouble from them either. They've got a lovely Siamese cat, Husch.
Before that, I lived in a shared house with two theology students and an older woman in her forties who used to write arsey notes instead of talking to you directly. In the kitchen, we all had our own allocated cupboards for our crockery and food, and she used to put her things amongst ours, then accuse us of stealing! Luckily, the landlord knew it was bullshit but this is why I'll take living on my own any day.