"Thousands waited in the rain on November 22, 1963, to catch a glimpse of him and First Lady Jacqueline Kennedy." [Dallas area prepares for 50th anniversary  of Kennedy assassination].
See the New York Times front page for that day and for the day that Oswald was killed. It is easy to see how conspiracy theories were born. See the Wikipedia entry. There were thoughts too that Vice-president Johnson was involved. Of course Fidel Castro and the mafia were suspects too. The Warren Commission to investigate the assassination did little to eliminate the various theories.
And there were too those that doubted that Oswald could have made that shot, but see this [thanks to Jack Bog's Blog] cam set up at Dealey Plaza. Maybe it is the optics - but that doesn't look like a difficult shot.