If you think you're the best at using a micrometer, challenge your friends to a micrometer race. Each person gets a micrometer and a different length of a wooden dowel. Race to be the fastest one to measure the dowel within a given error margin. Repeat with several dowels of different widths, and keep score. The first player to get three points wins the race.
There are actually many different kinds of micrometers. In this game, you can test people's knowledge about what different micrometers are used for. The most commonly used micrometers (used in these games) are outside micrometers, which measure the width of a thin object. Inside micrometers measure hollows in objects. Screw micrometers measure the pitch diameter of a screw and depth micrometers measure the depth of a hole or indentation. There are also lesser known micrometers, such as blade and disc micrometers. Create a game by describing a micrometer and asking players to guess which type of micrometer it is. You can also show players an example of various types of micrometers and see if they can identify them.
Collect various regular objects with small widths before playing this game. Each person estimates how many millimeters wide each object will be. The "judge" of the game then measures precisely how wide the object is using a micrometer. The player whose answer is most nearly correct gets a point, and the player with the most points as the end of the game wins.
For students, or people who are just starting to learn how to use a micrometer, measuring anything accurately can be difficult. To give them plenty of time to practice, challenge them to a game called "Get It Exact." Players try to measure to same object and see who can get closer to the predetermined measurement (which you should have ready beforehand).