A variant of that game that I've played a lot is to write a sentence, then next person draws that sentence in pictures and folds (hides) the sentence part, next person needs to verbalize the picture again and fold the previous part etc. Often the end result is hilarious.
One that I don't see - or maybe I don't know what I'm looking for - is "Fish, Fruit, Flower"[0], which we used to play as a family when I was young.
[0] http://www.lingolex.com/alfgame.html