When you select "Shut Down" from the Start menu, a dialog appears with three options: "Stand By", "Turn Off" and "Restart". To get the secret fourth option "Hibernate" you have to press the shift key. Would the Alt key be the more obvious choice for revealing alternate options?
You might think so, but it so happens that Alt already has meaning. In this dialog, the Alt key would be a disaster, because the underlined letters indicate keyboard accelerators, which are pressed in conjunction with the Alt key. In other words, from the Shut Down dialog, you can type Alt+S to stand by, Alt+U to turn off, or Alt+R to restart. Since the Alt key was already taken, the Shift key had to be used to reveal the bonus options. Using the Shift key to reveal bonus options is not uncommon. You can hold the Shift key while right-clicking on a file to get an extended context menu, and of course there's the Shift+No option in file copy dialogs to mean "No to all".
In fact, you don't need to press the Alt or Shift keys at all. Recall that the rules for dialog box navigation permit omitting the Alt key if the focus control does not accept character input; since the only things on the Shut Down dialog are pushbuttons, there is no character input and you can just press "S", "U" or "R" without the Alt key. What's more, you don't need to hold the Shift key if you want to shut down; you can just type "H" and the Hibernate option will be invoked, because hotkeys for hidden controls are still active.