The time that crossed the line: Poland wanted to declare war on Greece, no one else wanted to get involved on either side, and it was a pretty even match between them.
A friend not involved in this game was visiting family in the same city as the Greece-player, so we knew he'd be dropping by to visit him too. Poland-player told the "neutral" friend: if Greece-player shows you his civ game, take a picture of the screen when he's not looking and message it to Poland-player.
Well he did it, Poland declared war, and his knowledge of the position of troops lead to him winning the war.
"How did you know I didn't have any troops in my southern cities?" And Poland told him how he knew. It didn't end the friendship but there was about a month of not talking to any of us. When he cooled down there was a long meeting over whether that was cheating or "All is fair in Love and Civ". We could never come to a real agreement, 3 in favor of cheating, 3 in favor of dastardly but legal. But we now have an explicit rule of no screen sharing of any kind.