The game originally was going to be set in a more modern theme and Link would have the ability to travel to the future. The Triforce were also going to be computer chips instead of artifacts and Link's name was supposed to have meant a "link" between the present an the future. Today, Link's name is means a link between the game and the player.
There was going to be Christianity in the Zelda mythos, but the idea was scrapped and the goddesses were used later on. However, the cross is still used as a design on Link's shield and on the Book of Magic, which is a Bible in the Japanese version.
The first old man in the game offered a choice between the weakest sword and the weakest boomerang earlier in development, rather than just the former as seen in the final version. His text matched this choice and Clyde "Tomato" Mandelin's first "Legends of Localization" book translates it as "It's dangerous to go alone. Take the weapon of your choosing."
At first, Koji Kondo wanted to use an 8-bit rendition of Maurice Ravel's Bolero as the Title Screen theme. However, the tune wasn't in the public domain back in 1986 yet, and Nintendo didn't want to pay the rights. So he modified the timing of the "Overworld" theme and used that instead. And the rest is history.