British Bulldogs.
Start with a small team of "bulldogs" in the middle of the field. Everyone else tries to cross the field without getting taken to the ground by the bulldogs; anyone who does joins them. The winner is the last one to not be a bulldog. Extra points if they make the last crossing solo.
It kept getting banned at school due to the injuries so we renamed it multiple times to stuff like African Lions. It was the best game.
Capture the flag was the ultimate game in elementary school PE.
It had strategic planning, feats of athleticism, and individual moments of heroism and sacrifice.