My brother-in-law's family does this.
All the boys have the middle name
George, no exceptions. They have been doing it for several generations (at least 4 that he knows of). I think it's really cool actually, but hard to accomplish because there is always that parent who doesn't want to follow the tradition and it's broken.
It's pretty impressive the longer the tradition goes.
I don't know any girls who share middle names though.