Magical Sword

The Magical Sword is the final and strongest of all three swords in The Legend of Zelda. In the first quest, the sword is in the posession of an old man who lives under one of the graves of Hyrule's cemetery, but will only part with it once Link's health bar has 12 Heart Containers.

It is assumed that this is the sword wielded in The Adventure of Link as well.

There is a some debate as to whether or not the Magic Sword is in truth the Master Sword. although there is no proof whether these swords could be the same or not, other than a difference in their name.

Soulcalibur II
In the fighting game Soulcalibur II Link made a special guest appearance as a fighter. One of his weapons was the Magical Sword, and although it looks different from the original images of the magical sword (having a purple hilt like the Master Sword and the Triforce on its hilt), it still bears its name. The Magic Sword is capable of piercing defenses, but the Magic Shield it is paired with apparently hasn't held up as well, and is slightly weak to impact.

Trivia

 * It has been thought that the Hero's Spirit's sword is the Magical Sword. However upon closer observation, it doesn't look exactly like the Magical Sword.
 * In The Wind Waker, when Link travels to Hyrule Castle to retrieve the Master Sword, several statues will be holding weapons that look similar to the Magical Sword.