We have our photo competition, which is still going after more than 2 years.
We have had a few answerathons, which are great but do require daily activity and do not suit all of our users. (Answer an older question and get it upvoted you get 48 hours to answer and post it) and the winner is the one who manages to do it longest.
I would love to see a different kind of competition, one that everybody has a chance to participate in and one that is not going to be won automatically by someone who has been around for a long time. But I am out of ideas and ask the community for ideas.
If you know of a Stack Exchange site with a good competition which would fit here, copy/steal the idea, adjust it and post it here.
Or think up a new competition.
If you have an idea, please add how often you think we can run this competition, like once a day, week or month, only once, or regularly?
Other answers, why you do not want a (new) competition are also welcome.