Kid, I'm with you.
I've lived in my current house for 6 years, and I know the neighbors on either side. I've met two other neighbors across the street, but I don't ever see them. I know one of them has a child. I don't ever see that child out and about.
Last month my husband and I were sitting outside one night and talking about the disconnect we feel with our neighborhood, and the fact that we don't feel like we live in a community so much as a collection of houses. We thought about organizing a neighborhood block party at the local school, and even decided we'd go around knocking on doors, talking to people and inviting them to the party. We reached out to our local representative, never heard anything, and then realized how much work it would be to organize and pull of everyone on our own.
I would love to live in the kind of neighborhood I did as a kid - the kind of place you described, where people knew and looked out for each other. We're looking to move over the next year, and a big part of our decision on where to buy next will be what we see when we drive around the neighborhood on a Saturday morning or Monday afternoon.