In Queens in the 60’s, we played the five box
version of boxball described above. Two players
stood with five boxes between them; you would first bounce it once in the box closest to your opponent (your fifth box), and then once in each of your fourth and fifth boxes, and so on. I’m not quite sure if I remember the ping-pong style of two box that Connie describes above.

We didn’t play hit the stick, but I do remember playing hit the penny. I think you scored one point if you hit the penny, and two if you flipped it. Players stood with two boxes between them, and
put the penny or other coin on the crack between the two boxes. We didn’t like to use nickels because they were heavy and more difficult to flip. :^) This was a mostly a game for younger kids, whereas I remember still playing boxball
into early adolescence, when we weren’t playing
wiffle ball or stick ball or just hanging out.

Another favorite game of childhood was ring-o-levio, which I played from early childhood right through high school. Those later HS games
were neighborhood-wide.