Not sure if this is really a "game", but it's fun and this is the best place for it.

What are your extreme lights? The most northerly, southerly, easterly, and westerly ones you have seen? What about the tallest? The shortest? Whatever you can think of...the only requirement is the N/S/E/W, and then you can do whatever you want.

Mine:

NORTH: Annisquam Light, Rockport, MA
SOUTH: St. Simon's Island Light, St. Simons Island, GA
EAST: I think it's Chatham, MA, but not sure if Nauset or Highland are more east.
WEST: Barcelona Light, Westfield, NY

Other stuff:

Tallest: Cape Hatteras
Shortest: I think it's Derby Wharf, MA
Oldest: Sandy Hook

I'll edit this post if I can think of more later.