It's a coincidence that doesn't happen very often, a run of the same digits when you write out a date numerically. You probably remember 9/9/99 even if you can't recall what you were doing on that day. (Some of you might even remember 7/7/77. Or 6/6/66.) 8/8/88 was the day that Archie Harrison, a gay man with AIDS whom NPR was doing an ongoing series of stories on, died from that disease.
When summed together, the digits of 11/11/11 add up to the number 6. 111111 in binary gives the number 63. I'm no numerologist, I'm just sayin'.
The number eleven seems to crop up in news of significant events. Today we commemorate the 93rd anniversary of the end of the first World War, which occurred at 11 AM on 11/11/1918. The coup d'etat led by general Augusto Pinochet which ousted democratically-elected Chilean leader Salvador Allende and put in its place what was arguably the worst dictatorship since Hitler occurred on 9/11/1973. Of course I don't have to tell you what happened on 9/11/2001. The Soviet Union, our Cold War adversary, stretched across 11 time zones. And just to ice the cake, on December 11, 1990, there was a massive pile-up involving 99 vehicles along Interstate 75 near Calhoun, Tennesee; 99 is the product of eleven times nine. (Cue: Theme from The X-Files).
There's something about certain numbers that makes even seemingly rational folks go into supermarket-tabloid mode. On 12/21/12 (a palindromic date listing, no less!), the Mayan calendar reaches the end of a major cycle. Many folks, most of whom it is safe to say are not Mayans, see this as the official date of the End of the World, just as folks did in the year 1499 when thousands believed that the calendar rolling over into the year 1500 would usher in the apocalypse. (I've often wondered why none of these kinds of numbers ever seem to augur anything pleasant. or at least harmless).
Just for giggles, does anyone here still remember “Y2K”? Power grids were supposed to go down, nuclear power plants would all melt down simultaneously, missile launching systems would go out of control and computers everywhere from government agency mainframes to home desktops would go berserk. The only indicator of that event that I observed was when a few web sites I went on listed the year of the current date as "19100". (Hey, politically isn't it nineteen-eighty-thirty-one in America?)
Now if you'll excuse me, I've got to put these groceries away. How much did I spend on 'em anyway? I was in a hurry and just handed the cashier a twenty-dollar bill, pocketed the change, grabbed the bag and made the bus home just in time. Oh, here's the sales slip. What was the total? $11.11...hmmm...(cue: theme from The Twilight Zone)