These items will appear on the equipment subscreen, but can't be "used" like swords or shields, they improve Link's abilities automatically. For heart and power upgrades see Heart Containers and Fairy Fountains. In some instances such as the Bomb Bag upgrade, the order in which you received the upgrades can be reversed. The list provided is the most sensible way to go about things but it can be approached backwards as well.
Heart Containers and Piece of Hearts
Throughout the game you will pick up Heart Containers that increase Link's health by a whole heart. This enables him to take extra damage before dying. You can get even more heart containers by finding four Piece of Hearts (a.k.a. heart pieces). The locations of these are noted here.
Wallets determine the maximum amount of rupees Link can carry. He starts out with the Child's Wallet, which maxes out at 99 rupees. He can later obtain the Adult's Wallet (cap. 200) and Giant's Wallet (cap. 500) through the Gold Skulltulas sidequest.
All three strength enhancers give Link strength to lift things he normally wouldn't be able to. Some just make Link stronger.
This small golden bracelet is given to Link as a child by Darunia, the leader of the Goron tribe. It is needed to pick Bomb Flowers, which are needed to enter and traverse Dodongo's Cavern. When Link becomes an adult, he no longer needs the bracelet, as his maturity has given him enough strength to pick the explosive plants by hand.
These gauntlets are given to Link as an adult when he helps Nabooru. They are silver-plated gloves with flashing red magic gems that enhance his strength. They allow link to lift giant blocks. They also let Link lift heavy gray boulders. However, Link cannot move under the weight of them.
These shining gloves will allow Link to lift objects with superhuman-like strength; however, only a handful of objects need these in order for Link to lift them. For instance, when you enter the castle of Ganondorf, in order to break the Fire Seal protecting the tower, in the room where it is necessary to retrieve silver switch crystals, one of which is covered by a giant rock pillar that you need the gloves to remove.
Scales are magical items from the Zora tribe that allow Link to dive deeper than he would normally be able to.
This scale enables Link to hold his breath underwater for five seconds, allowing him to dive deeper than before. Complete the Diving Minigame as a child to earn this item.
This item allows Link to hold his breath underwater for nine seconds. This can be a handy ability, although it is unnecessary to complete the game. The Golden Scale can be obtained by catching a fish of 13 pounds or more in the Fishing Pond as an adult.
Quivers hold the arrows Link uses with his Fairy Bow. When he first obtains the bow, he inherits a regular Quiver which lets him hold 30 arrows, but larger quivers can be found later in the game.
This replaces the regular Quiver that came with the Fairy Bow, and allows Link to hold up to 40 arrows. It can be obtained by clearing the Shooting Galley minigame in Kakariko Village as an adult.
This replaces the Bigger Quiver (or regular Quiver), and allows Link to stock up to 50 arrows at once. It can be obtained through the Horseback Archery minigame in Gerudo Fortress.
Link finds his first Bomb Bag in Dodongo's Cavern, which enables him to use and hold up to 20 bombs. Other bags can be found later which hold even more bombs.
When Link is a child, if he stops the Goron rolling around Goron City, the "Hot-Rodder Goron" will award Link with the Bigger Bomb Bag. To do this you must place a bomb in his path, or send a bombchu flying his way. And, he must be within the tunnel when you stop him. This will replace his regular bomb bag and allow him to carry up to 30 bombs.
This can be obtained as one of the random prizes from the Bombchu Bowling Alley in Hyrule Castle Town or Kakariko Village. It will replace the (Bigger) Bomb Bag and allow Link to hold as many as 40 bombs.
Deku Seed Bags
This bag holds Deku Seeds to be used as Slingshot ammunition. Link receives the smallest Seed Bag, capable of holding 30 seeds, when he finds the Slingshot.
To find the bigger Deku Seed Bag, enter the Lost Woods and go right. You should see a tree with a target hanging from it. Use your Slingshot to hit a bulls-eye three times in a row and you will receive a bag worthy of holding up to 40 seeds.
This replaces the (Bigger) Seed Bag that came with the Slingshot, and allows Link to hold up to 50 seeds. It can be obtained by clearing the Shooting Gallery minigame in Hyrule Castle Town as a child.
These side quests can be completed in reverse order, where completing the Shooting Gallery minigame will upgrade your capacity to 40 seeds, and hitting the bulls-eye three times will upgrade you to 50 seeds.
Deku Stick Capacity
Technically, this doesn't appear anywhere on the subscreens, but the amount of Deku Sticks Link holds can be increased like Bombs or Arrows. At the game's start, he can hold up to 10.
Enter the Lost Woods and go left, left, to the room with the bridge exiting Kokiri Forest. Go to the opposite wall to find a Deku Salesman who will bestow you with the ability to carry 20 Deku Sticks for 40 Rupees.
To carry 30 Deku Sticks, first borrow the Skull Mask from the Happy Mask Shop. Then go to the Lost Woods from Kokiri Forest and go right, left, right, left, left. In this room is a lone tree, to the left of which are a number of butterflies hovering over a grotto hidden by the grass. Walk around this area until you find the grotto and enter "The Forest Stage." Put on the Skull Mask and step into the spotlight. The Deku Scrubs will like your mask and enable you to store 30 Deku Sticks.
Deku Nut Capacity
Like Deku Sticks, the maximum amount of Deku Nuts Link can carry can be upgraded throughout the game, but there aren't items representing it like the Quiver or Bomb Bag. When Link first obtains a Deku Nut, he'll be able to store up to 20.
First, get the Mask of Truth from The Happy Mask Shop. Then go to the Forest Stage in Kokiri Forest: from the start of Kokiri Forest's maze go right, left, right, left, left. In the back of the room above the grass, you'll see some butterflies flying. There is a hidden hole under them. Enter it and put on the mask. Walk up to the scrubs and they will have varying reactions. Present the mask until they offer to increase your Deku Nut capacity to 30.
One version of the game allows you to still obtain this upgrade after becoming Adult Link. To do so, find the room containing two Business Scrubs, a patch of soft soil, a large field of grass, and a tree. Look through the Mask of Truth. Above the grass, you'll see some butterflies flying around near a hole. Enter it. Put on the mask, and walk up. The Scrubs will look at you. Walk up to the Scrub with the mustache and talk to him. He will give you the upgrade.
To further increase your capacity, go to the room in the Lost Woods with the entrance to the Sacred Forest Meadow. There, destroy the large rock and enter the grotto. The Business Scrub there will bestow Link with the ability to carry 40 nuts (at a cost of 40 Rupees for the upgrade).