Shigeru Miyamoto, the creator of the Legend of Zelda, grew up in a small town in Japan. His family didn't own a TV, so he spent most of his days exploring the countryside. One day he stumbled upon a miniature cave system. This would lead to the inspiration to create the game many years later. Just think if Miyamoto's parents had owned a TV we may have never gotten the Legend of Zelda series.
Both the Legend of Zelda and Super Mario Brothers were being created at the same time. Anytime a new element to one of the games were being considered, Miyamoto decided whether or not it was more of a Zelda element or a Mario element. This lead to some things ending up in both games. In Zelda, the enemy known as Manhandla is a four-headed piranha plant which look almost identical to the Mario plants.
Originally, you started the game with the sword. However, during focus testing too many people complained that the game was too difficult and that they had no idea where to go or what to do. Miyamoto decided to make the more difficult rather than easier, and one of the changes was to start the player weaponless and make them find the sword. The thinking behind this was to make the gameplay more communication based, and in the pre-Internet world, this meant comparing notes and sharing secrets with friends. Anyone who grew up in the '80s knows that the Legend of Zelda was one of the most talked about games on the school playground.
The game was originally titled the Hyrule Fantasy in Japan, with the Legend of Zelda serving as the subtitle. When the game was ported to North America the Hyrule Fantasy was dropped and the Legend of Zelda became the title. This lead to the Hyrule Fantasy name being phased out quickly in Japan as well.
The game originally started out as a dungeon building sim. The Legend of Zelda started on the Famicom Disk System, which featured rewritable floppy disks. To take advantage of this feature, some early versions of the game allowed players to design and share their own dungeons. Eventually this feature was dropped.
After you defeat the game, you unlock a second quest. This is actually pretty well known, as well as the fact that you can go straight to the second quest by entering Zelda as your name. However, what's not as well-known is the only reason the second quest exists is due to a programming mistake. It turns out that once the game was almost finished the developers realized it only used about half of the data they thought it would. It was Nintendo's policy to use as much of the available cartridge capacity as they could, so they decided to double the length of the game to use up that storage space.