Lantern

The Lantern has had various different incarnations in its history, with its first appearance in 'A Link to the Past''. The Lantern is used to light up dark places and dungeouns, ignite torches to solve puzzles, and burn shrubbery and grass to reveal pathways, or sometimes just rupees. The item took a back seat in some major console titles such as and Ocarina of Time, with a larger emphasis given to Fire Arrows, but resurfaced in full 3D glory in  to much success and usability. The lantern (or an equivalent item) has been included more often than not in the 2D iterations of the series.

A Link to the Past
The Lantern is the first item Link will find during his quest in 'A Link to the Past'', located in a chest inside Link's house when the adventure first begins. Using the Lantern consumes Magic Power, so Link must use it sparingly.

Four Swords Adventures
Specifically called the Lamp in Four Swords Adventures, this item is not a part of Link's permanent inventory. The lamp instead appears whenever it is necessary, whether it be a dark dungeon, or in the face of a torch puzzle. The lamp also functions as a prevalent, lethal weapon against Jalhalla. Link needs no consumable fuel to operate this lamp, as he does not carry it on his person.

The Minish Cap
The Flame Lantern is a simple lantern received by Link in the Temple of Droplets in The Minish Cap. The Flame Lantern lights up a moderate area around Link, and also is used to melt ice and light lamps. The Flame Lantern is essential in the battle against the dungeon's boss, the Big Octorok.

Twilight Princess
Early during his quest in Twilight Princess, Link can obtain a lantern from Coro in Faron Woods. The man gives Link the lantern as part of a business plan to boost sales of his main product: Lantern Oil. Unlike previous incarnations, the Lantern can be hung from Link's belt while lit, allowing the hero full use of his hands, while still providing him a source of light. If Link brandishes the lantern while there are Poison Mites nearby, the flame will keep the annoying vermin at bay, preventing them from impeding his progress.

Unlike previous Zelda games, where lanterns used magic power to fuel themselves, the lantern in Twilight Princess is fueled by lantern oil, which can be purchased at various shops or found in dungeons. Link can also substitute yellow Chu Jelly, obtained from yellow Chus, to fuel his lantern. Link can store extra fuel for his lantern in an Empty Bottle.

Trivia

 * The Lantern appears in, but only as a light source that hangs from the ceiling in the Forsaken Fortress, and inside various Submarines and dropholes scattered about the Great Sea. It is not an item Link can physically equip.