This one has given us lots of fun: the detective, as we love devising riddles and puzzles. Each person has a turn to be the detective, who leaves the room while their mission is agreed upon, which might be "find out what colour socks mum is wearing", with a time limit, say ten minutes. The detective is then blindfolded and brought back in, and told their mission. The detective asks questions, which can only be answered by yes or no. There is usually a catch, which might be that mum is not wearing any socks. Can the detective work that out? 
If the detective is struggling, hints can be given halfway through the mission's time limit, especially for younger detectives. Only the person who thought of the question is allowed to give hints.
Missions we have used have included:
If you could see through your blindfold, find out whose face would you be looking at. (Their own face in a mirror.)
What colour are the balloons on your party hat? (The hat has many decorations, but no balloons.)
Where is a small object hidden in this room? (Inside the detective's blindfold.)
Who stole the Christmas Pudding? (Rather than asking "was it mum", the detective is encouraged to ask questions of everybody such as "was the thief male". The answer is that everyone thinks it's the person on their left. Or the answer could be that the Easter Bunny stole it.)
What is on your finger? (Something sticky, such as chocolate, is put on the detective's thumb. The right answer is not the chocolate, but their rings!)
Any many more!
We have forfeits to keep the non-detectives on their toes: players who giggle excessively miss a turn answering a question. Players who give anything away are blindfolded until the mission is over.