(As a side note, there are a number of posters out there for this film, but I'm not a fan of the more modern DVD box posters - I prefer vintage posters like this one.)
The most expensive black-and-white movie ever made at that point, The Longest Day was an immense undertaking. Thousands of extras were used for the Normandy invasion sequence, and while excavating along the Normandy beach for the making of the film, an intact Allied tank was discovered, buried in the sand. The tank was excavated, repaired, and used in the film - quite the feat of engineering and restoration!
One of the most interesting things about this film is that so many of the people involved with, or consulted on the making of the film were actually involved in the D-Day invasion, and not just British or American troops, but Germans and Frenchmen as well. The film was truly an international undertaking, with American, German, and British film-makers filming the sequences involving their respective nationalities.
There is so much trivia involved in this film, I won't go on here any longer. You can view the film's entry on IMDb as well as its Wikipedia article for more information.
Here's the trailer for The Longest Day. There are other portions of it on Youtube, but sadly it hasn't had as much of a presence there as other war films. I wish I could find a sequence for the assault on Pegasus Bridge, but I don't see it out there anywhere - if someone has better luck, please post a link in the comments section!