Quiver

A Quiver is a specialized bag that holds only arrows, for use with a bow. Capacity varies, but in the majority of Zelda games, the quiver can be upgraded after completion of sidequest events at least twice over the course of the game.

Not all games that include arrows mention a special bag for them. In A Link to the Past for example, a Great Fairy can increase Link's arrow carrying capacity, but the game never specifies how.

Ocarina of Time

 * Basic Quiver: When Link retrieves the Fairy Bow from within the Forest Temple after defeating some Stalfos, the weapon by default comes with the basic quiver, an arrow bag that can hold up to 30 arrows.
 * Big Quiver Upgrade: In Kakariko Village, the building that was being built in the past is now the Shooting Gallery. To win, Link must successfully shoot all ten rupee-shaped targets in succession (some of which move) from fifteen shots, with eight or nine out of ten giving a free retry. Upon winning, Link receives the Big Quiver Upgrade, a bag that has the capacity to carry 40 arrows.
 * Biggest Quiver Upgrade: In the Gerudo's Fortress, there is an archery range. Getting at least 1000 points gets Link a Piece of Heart, while getting at least 1500 gets him the Biggest Quiver, a bag that has the capacity to carry 50 arrows.
 * Note: These two upgrades can be obtained in either order.

Majora's Mask

 * Basic Quiver: When Link retrieves the Hero's Bow from within the Woodfall Temple after defeating a Dinofols, the weapon by default comes with the basic quiver, an arrow bag that can hold up to 30 arrows.
 * Big Quiver Upgrade: In Clock Town, their is a Shooting Gallery. To win, Link must successfully shoot the red Octoroks. Breaking the high score gets him the Big Quiver Upgrade, a bag that has the capacity to carry 40 arrows.
 * Biggest Quiver Upgrade: On the path to the Southern Swamp, there is another Shooting Gallery. To win, Link must shoot all the Guays, Mad Scrubs, and Wolfos. Upon winning, Link receives the Biggest Quiver, a bag that has the capacity to carry 50 arrows.

The Wind Waker
Although the basic quiver isn't shown as a physical item in The Wind Waker, Link can carry 30 arrows as soon as the Hero's Bow is obtained; the bigger quivers are received from two yellow colored Great Fairies located (respectively) on Western Fairy Island and Thorned Fairy Island. The first upgrade supports up to 60 arrows, the second upgrade supports up to 99.

The Minish Cap
There are three quiver upgrades in The Minish Cap which may be obtained in any order. The arrow carrying capacity increases from 30 to 50, 70 and finally 99.
 * Basic Quiver: When Link obtains the Bow from Castor Wilds, it comes with a quiver that carries 30 arrows.
 * Upgrade 1: A larger quiver of can be bought from Stockwell's Shop in Hyrule Town for 600 Rupees.
 * Upgrade 2: Another quiver upgrade can be found by climbing a beanstalk and opening a chest after fusing Kinstones with a Minish near the beginning of Wind Ruins.
 * Upgrade 3: An even larger quiver can be obtained by answering the Great Dragonfly Fairy's questions correctly. She is found in the Royal Valley.

Twilight Princess

 * Basic Quiver: When Link retrieves the Hero's Bow from within the Goron Mines after defeating the dungeon's miniboss, the weapon by default comes with the basic quiver, an arrow bag that can hold up to 30 arrows. From this point on, arrows can be hybridized with bombs to create Bomb Arrows, or with the Hawkeye to enhance shooting precision. On the Wii the bow is used with a cross-hair to enhance shooting accuracy. The GameCube usage of the bow/arrows is no different than Majora's Mask or Ocarina of Time, as somewhat of a first-person shooter.
 * Big Quiver Upgrade: In the only back alleyway accessible from West Hyrule Castle Town, within a circus tent there is a sidequest minigame called the STAR Game. The object of this game is to use the Clawshot to collect all of the glowing orbs within the cage within the limited time provided. Although Link can try again as many times as it takes to win, there is only one prize, this round anyway. Upon winning, Link receives the Big Quiver Upgrade, a bag that doubles carrying capacity to 60 arrows.
 * Giant Quiver Upgrade: After retrieving the Double Clawshot from the City in the Sky, the STAR game can be played again, but with more orbs, and no landing platforms for leverage. If Link manages to win once more, the prize is the Giant Quiver Upgrade, the largest bag which increases the capacity to 100 arrows.

Phantom Hourglass

 * Basic Quiver: When Link retrieves the Hero's Bow from within the Temple of Courage, the weapon by default comes with the basic quiver, an arrow bag that can hold up to 20 arrows.
 * Big Quiver Upgrade: In Molida Island there is a Shooting Gallery. This version of the Shooting Gallery slightly varies from its previous counterparts in that the score for successfully shooting a target is not fixed; rather, upon shooting the first target, Link gains 10 points. The second successive target shot will get 20 points, and so on until 50 points. Missing a target, or shooting the "little girl" target, will reset this back to 10 points, and the climb to 50 must begin again. Upon achieving a decent score, Link will receive a Big Quiver Upgrade, a bag that has the capacity to carry 30 arrows.
 * Biggest Quiver Upgrade: For the final quiver upgrade, Link just needs to buy it from any store for 1000 rupees. This quiver has the capacity to carry 50 arrows.

Spirit Tracks

 * Basic Quiver: After Link beats the mini-boss in the Fire Temple he gets the Hero's Bow along with the basic quiver that can hold up to 20 arrows.
 * Big Quiver: In Goron Village Link can buy a Quiver in the shop for 2000 Rupees, it can hold up to 30 arrows.
 * Biggest Quiver: Link has to score at least 3500 points in the Pirate Hideout minigame to get this quiver that can hold up to 50 arrows.