Moved here a couple years ago, initially met the neighbors and know their names, but haven't had more than a handful of couple sentence interactions since then.
On the one hand, I do want a little distance: I'm not trying to hang out all the time or necessarily make new best friends. But still seems like the neighborly thing to know each other a little bit more, to have someone to call in case of emergency, or hey your dog got out, hey the global order has collapsed let's band together to keep out the raiders, etc.
So interested to know, if you do interact with your neighbors, how did you get started? What is the extent of your interaction?
I just say hi and then maybe talk about their dog, my dog, or something else surface level.("How about those 'Sports Team Name'?", "You see that awesome new movie/show?", "Hey, did you hear about 'Local Event'?"). I stop to chitchat when I have time and I usually get to know my neighbors. We keep an eye on each others places/cars/etc., have taken care of their dogs while out of town and vice-versa and one of them is an emergency contact for my kids. Its way better to make friends than just be living close to a bunch of strangers. Not everyone is super social, but I still know pretty much all their names and they know me.