Jim K sent email pointing out it's “
Square Root Day,” 3/3/09. I guess the last Square Root Day was 2/2/04 (02-02-2004) and, as Jim points out, the next one will be 4/4/16 (04-04-2016). Oh, and I shouldn't forget the trivial solution, which was 1/1/01, the first day of the millenium!
Somehow I keep thinking it should be called Square Day.
So these were all repeated in the last century (which nearly all of us lived in, as strange as that still sounds to me). I was here for 8/8/64, 9/9/81, and 10/10/100, well, if you count 2000 in that Perlish way.