Battlestar Galactica is a great game for that
I forgot to mention the unspoken of phase. The crushing realisation that you have been betrayed/tricked, followed by the swearing, shouting and general falling out with the perpetrator (who either looks smug or a bit sheepish and apologetic)
If only real diplomacy was as civilised!
You run off into different corners of the house and have a lot of secret discussions. At the end of the allotted time you then go and write your orders (in secret), then either an "umpire" or through trust, you read out your orders in turn then resolve any conflicts.
I'd like to know how Diplomacy plays out in real life. I'm liking that we have no idea what anyone's really going to do at this stage, but surely you lose that aspect when facing other people?