I think people care less and less these days, especially if, like me, you live in an apartment.
I’m a fairly sociable guy generally, but I’ve never spoken to my neighbours, beyond “Hi” or a wave.
One time my neighbour was outside smashing up a computer hard drive with a hammer. I was curious…but not enough to have a conversation.
I don’t really care about my neighbors, but there is value in having an amicable relationship with them. For example, you’re about to go out of town and need someone to water your plants, depending on where your friends live and/or how convenient it is for them to help you (or if they even want to), you might come home to dead plants. Or if there’s an emergency and you or your neighbors need help, it’s nice to know that there’s someone right next door who can pitch in and help, whether that means calling the cops for you, being a “safe house” on the block for kids to come to if they get sent home from school in an emergency and their parents aren’t home or something else.
I don’t need to be buddy-buddy with my neighbors, but I do like that I know who they are enough not to feel like I’m asking a stranger for help should I need it. I hope they feel the same way.
It just makes life better if neighbors cooperate with each other. Examples:
When our snowblower broke last year, the neighbor across the street helped clear our driveway. This winter the man of the house across the street was away during one of our major snowstorms. My husband cleared their driveway. The lady of the house (don’t know if she’s wife or girlfriend) gifted us with huge boxes of fresh fruit. My son-in-law routinely clears the driveway of the elderly neighbor next door to him. They insist on paying him for it, although he doesn’t expect it, but it came in handy when he was temporarily out of work.
We have some elderly neighbors who were very kind to my late mother-in-law, and my husband routinely checks up on them, especially the ones who now live alone.
I suspect the OP’s answer depends a bit on whether the nearest neighbor’s front door is 5 feet, 50 feet, 500 feet, or 5 miles from your front door.
When I grew up neighbors were like 1 step down from family. Today I have a few neighbors I have close feelings for a vice versa but the neighbors from the past 20 years I don’t even know.
It’s just a law of physics. Tools are conserved.
My neighbors are my friends. I help them and they help me. We leave each other alone when help is not needed.
I’ll admit we live far enough apart that it would be hard to annoy each other even if we wanted to. And the immediate neighbors on each side of me are only here 1-3 months of the year. I might feel differently if the population density was much higher.
This!
It also depends on how you-all were raised. Country Vs. city. Eastern US, Vs. Deep south Vs. “mid-west” Vs. Western US, Vs. Southern California.
Western US, not to be confused with California. Please & Thank You!
Seriously, you did you not expect us to come up with “smart ass psycho answers” even when we were asked nicely not to? Really?? 
OH, I see that you have only been here for a few months. Well, OK then, nevermind.
Not everyone can afford a detached home and I think that would heavily impact the situation. I am very casually friendly with my next door neighbors now that I live in a house, but I absolutely hated my upstairs neighbors when I lived in a condo.
My new neighbor’s little dogs attacked my little dog the first time I met them. That left me with a bad taste re new neighbors. We do get along with all the other neighbors though.