Mario Kart on Facebook! Fast-spreading scam hits many users' Facebook accounts

A scam claiming that you can play Mario Kart on Facebook has spread between many Facebook users.
The messages do not just take the form of public status updates, but have also been distributed via private messages:

If you were fooled into participating in this scam remove the message from your newsfeed, and delete any messages you may have inadvertently shared with your friends. That way at least you are no longer spreading it with your online friends.