Unfortunately these days it seems that more and more people simply don't know their neighbours. We lead busier lives, and we're moving house a lot more than we used to. What's more, we're more connected to the entire world via our smartphones, so (sadly) we overlook our neighbours as "just other people". However, there's advantages to establishing good relations with your neighbours as we will highlight below.
When you know your neighbours, they're far more likely to watch out for your property if you're away on holiday. Of course, you should reciprocate when they're not home. A neighbourhood where everyone knows each other is a tougher challenge for burglars.
The neighbours have an advantage that Facebook can never compete with - they're in close physical proximity to you. If you do get on well with your neighbours, and you have enough in common with them, you might just find you've made some new friends who you can have a cup of coffee with at a moment's notice.
When your neighbours know you, it's more likely that they will consider you when it comes to noise pollution, building works and other possible nuisances. I know one neighbour who bought acoustic foam
for the walls of his bedroom music studio just because I'd introduced myself when I moved in. Prior to that, he never knew the previous neighbour and hadn't even considered noise pollution might be a problem.
Sometimes an entire community face a problem together. It could be vandalism, burglary or noisy drunks making a racket - these problems are more easily tackled as a community rather than as individual householders. By knowing your neighbours, you may well be joining the local community at the same time.
Disputes are more easily resolved
It's not like problems can never happen with your neighbour just because you introduce yourself and know them, but you're more likely to negotiate with them to a positive outcome IF there is a dispute. If you don't know them, then distrust can build up and when there's a problem, it may even be impossible to come to any kind of agreement (and so they escalate into legal battles).
It just feels right
This reason isn't so cut and dry, but nonetheless it's an important one: it just feels right to know your neighbours. Once you introduce yourself, a friendly "hello" when you see them is a lot easier than if you never introduce yourself. It just feels a lot more relaxed.