I would love to see a graphical replay of a full game after it is complete (a la Civilization).
As I envision it, there would be a starmap and a timeline (from the first to last tick). It could animate automatically at various speeds, or you could scroll through manually tick by tick. The color+shape of its current owner is the only info needed about each star. If a battle happens at a star on a given tick, there would be a little explosion or other graphic. This would scale up in size based on the number of ships destroyed (logarithmically, perhaps?).
Beyond that, it could be accompanied by graphs of various intel items, but the starmap+timeline alone would make for an awesome feature (and would be quite shareable!).