Broken Sword

The broken sword appears in several Zelda games.

Ocarina of Time
Also known as the "Broken Giant's Knife", the broken sword is the handle and portion of the blade remaining from the Giant's Knife. The remaining handle can still be used as a weapon, but will only inflict 1/4 the damage of the original Giant's Knife. If you return the broken sword to Medigoron, he will forge you a new one for 200 rupees.

However, if you perform a trading sidequest, you can get a more sturdy Biggoron Sword, which will not break.

Oracle of Ages
The Broken Sword is the last trading sequence item, and becomes the Noble Sword when you go with Patch to repair it at the Restoration Wall. You get it from the Old Zora in a cave near Rafton's House, in exchange of the Sea Ukelele.

The Minish Cap
Not so much referred to as the "broken sword", you recieve the broken handle of the Picori Blade early in the game, which Melari will reforge for you later in the game.