I'd love to be able to replay the turn my opponent has just taken. When it's my turn, I can only see where all units of all players are, what cities they conquered, etc. But I have no idea how they moved. In fact, I would love to be able to replay any turn of any player up to the actual turn. Fights should not be displayed as it would expose stacks' composition, but everything else should be displayed. By everything else, I mean armies moving. And that's all, I guess.
In FOW games, only those armies should be shown moving that I could see. Games could be then saved into an archive and players would be able to watch replays of good players and learn. Of course, watching a game already ended would display everything as no cheating would be possible.