Puzzle - All ages
I have used this idea many times with form groups as an end-of-term or one-off activity. Make up a wordsearch containing everyone's name except one person. Choose someone with a fairly short name (so that it is harder to spot its absence) and who you are sure won't mind - they can have a special prize at the end. Such puzzles are easy to generate by pasting the names from your class list into http:puzzlemaker.school.discovery.comWordSearchSetupForm.html.
Pupils are generally eager to do the puzzle and see who isn't there. You can add yourself if you wish and perhaps a random celebrity, so you have an extra challenge if there is a draw.
Pupils love it if you add other names, such as a pupil's pet who they are always talking about. One pupil was known to call his pencil case Fred, so I added Fred.
If you want to make it serious, you can discuss afterwards how it feels to be left out of something for an arbitrary reason - in real life, people can be left out of groups for the silliest reasons.
Colin Foster teaches at King Henry VIII School in Coventry.