A simple game like Dumb Charades (sometimes if modified a bit) is a great exercise in thinking and communication.
It can be played beyond movies into other things like contradictory/funny/naughty phrases, and it is not just a source of good fun, but a lot more. To give the phrase, one has to think hard and creatively to find something that is not just hard, but funny too. Something what advertisers are always trying to do. The next is to put yourself in other person's shoes and judge whether the word/phrase can be decoded easily by the rival or not.
On the other side of the game, having a phrase/word, you need to think of multiple ways to get the phrase communicated by breaking it down and expressing it logically to the team mates. You also have to read into their minds and see if they can interpret your expressions (again, putting yourself in other person's shoes) and then guide them towards the word.
Dumb charades is a great way to improve lateral thinking.