Lantern

Background
The Lantern has had various different incarnations in its history, with its first muse in the SNES title A Link to the Past. However, the item took a back seat in the major console titles, with a larger emphasis taken on Fire Arrows, used to create light or do damage to enemies. The lantern however, has been included more often than not in the handheld iterations of the series, including the latest The Minish Cap. The lantern also appears in Twilight Princess, but it requires Lantern Oil to use it.

A Link to the Past
The manual description :

This is the first item you are likely to find in your adventure, located in a chest inside Link's house. The lantern lights the torches in the dungeons and brightens the dungeon rooms, as well as burning bushes. It consumes Magic Power to light the torches, and they go out after a time.

Four Swords Adventures
Specifically called the "lamp" in game. This item is not a part of Link's permanent inventory. The lamp appears in stages which would require the use of it for completion. As in previous and following titles, the lamp is primarily used as a light source within a small radius of Link. It can also be used to set fires to torches, grass, wooden stumps, and some enemies. The lamp also is a potent weapon against Jalhalla. Link needs no consumable fuel to operate this lamp.

Twilight Princess
The manual description :

This item burns bright to light the area around you and provide you with a fire. You can use other items while using the lantern. The lantern is vital to the completion of nearly every temple throughout the game, especially since specific portions of them include pitch dark passageways.

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 found at various shops or received from the jelly remnants of yellow ChuChu jelly.