This is not the first time that such rumors have been spread. Somehow we survived the Mayan calendar, and before that the turn of the millenia. I remember Nostradamus predictions being quite popular back when I was a high school student. I know people who try to cross-reference the world news with the Book of Revelation. Yet somehow we are still here (with the exception of those of us who aren't).
Despite my reassurances, some students remained adamant. They noted Bible verses that predict the end times with chapter and verse numbers that matched the dates of recent hurricane landings. They said that the recent earthquakes in Mexico were on the anniversary of other devastating earthquakes (the odds aren't all that astronomical). Even an acquaintance of mine predicted today that Alaska would be seeing an earthquake of 7.0 or higher in the next sixth months as a reaction to these other natural disasters.
In the end, I told my students that they should do their homework anyway ... just in case we are still here on the 24th.