Well, it's not the coolest, but it's definitely funny (to programmers).
We built an ad-hoc query builder for a resume database project. There were some ajaxy parts to it and the basic idea was that if you changed anything on the page, the search automatically re-ran itself. (It was triggered by the onBlur event of all the UI widgets)
So we had no real use for a "Search" or "Run Query" button. This confused the users to no end. So we added a search button which did nothing. It just sat there.
It worked because every time you clicked the search button, the onBlur event from the field you were just on would fire.
This made our user base very happy. Simple things.