Organize a block party. I didn’t learn most of my neighbors’ names until we had our first block party. After that one party, it seemed there was a lot more interaction on our block. This one does involve a little work, but if you share the coordinating duties with other neighbors and keep it simple (at least that first year), this is an easy way to get to know your neighbors.
This works on the neighborhood level and with other types of communities, as long as people are close enough to interact with each other fairly often.