The funniest D-Day movie, by far, is Paddy Chayefsky's satirical
The Americanization of Emily (1964 - Arthur Hiller) starring James Garner as the man a crazed Admiral hand-picks as the designated first casualty of the invasion. And maybe the most unconventional movie using D-Day as a back-drop also stars Jim Garner:
36 Hours (1965 - George Seaton), where his Intelligence Officer is captured a few days before the invasion and put through an elaborate ruse by the Germans to trick him into revealing the details. Also the thriller
Eye of the Needle (1981 - Richard Marquand) cleverly uses the run-up to D-Day, as Donald Sutherland's Nazi spy discovers the dummy wooden tanks used by the Allies as a decoy to make the Germans think Patton would be leading a later landing, but finds himself trapped on a remote island off the coast of Britain and tangled up with the family that lives there. Will they discover who he is before he kills them and gets his information back to Germany? Good adaptation of the Ken Follett novel.
A good little-seen one of boot camp and the battle itself is
Overlord (1975 - Stuart Cooper) which ingeniously blends stock footage to give an air of documentary-like authenticity.
Overlord has a well-earned cult reputation, but it should be relatively easy to find in the U.S. now thanks to its DVD release last year as part of the Criterion Collection. Anyone who has seen the excellent IFC documentary
Z Channel: A Magnificent Obsession (2004 - Xan Cassavetes) may remember it being featured there as well.