In many countries*, the shortest hour starts at midnight (or rather, just after 23:59:59)GMT, on the last Sunday of April (October if you live in the Southern hemisphere). Thanks to Ben Franklin's energy-saving concept, Daylight Saving Time, the hour passes in an instant as nearly half of the world switches to summer time.
* Refer to http://www.worldtimezone.com/daylight.htm for an exhaustive list.
Update: as of January 2004, the writeup above is no longer there, unlike its softlinks. I apologise to everyone troubled by this node hi-jack.