In Majora's Mask Link can acquire many items on his quest, many are the same as Zelda 64, but there are some different one's unique to Majora's Mask. Most of the items have the ability to be carried with you back in time.
Razor Sword - If you give the Kokiri Sword and 100, rupees to the Mountain Smithy and they will forge it for you. This sword is double as powerful as the Kokiri Sword, but will break after 100 consecutive clangs. It also can't be taken back in time if you go back in time.
Gilden Sword - You will have to Forge the Razor Sword, then give it and the Gold Dust from the Goron Races to the Mountain Smithy. This one is three times as powerful as the Kokiri Sword and doesn't break. It can even be taken back in time with you.
Great Fairy's Sword - Collect all 15 of the stray fairies ini the Sonte Tower and take them to the Ikana Fairy Fountain and you will be rewarded with this two handed sword. It has many simlarities to Biggorons sword from Ocarina of Time.
Mirror Shield - This one is in a treasure chest at the end of the bottom of teh Well dungeon. This shield can be used to relect sunlight as well as certain kinds of attacks.
Hero's Bow - If you defeat the Lizalfos in Woodfall Temple you will be rewarded with this item. It allows Link to use Arrows that can fire at distant objests like switches.
Hookshot - This can be found at the Great Bay Gerudo Fortress. It allows Link to grapple things and pull himself across gaps that he might not otherwise be able to cross. Pretty much the same thing as Ocarina of Time.
Fire Arrows - If you defeat the Wizrobe in Snowhead Temple you will receive this item. Same thing as Ocarina of Time pretty much although these may find a little more use in Majora's Mask.
Light Arrow - If you defeat Garo Master in the Stone Tower Temple you will be rewarded with this. Light arrows are used to destroy sun blocks and sun switches and are useful against undead enemies like ReDeads.
Ice Arrows - If you defeat Wort in Great Bay Temple you will get these. They allow you to make ice bridges to cross areas of water. a different ability than Ocarina of Time.
Ocarina of Time - You will pretty much automatically get this one just by going to the final night in the first part of the game, and when you shoot a spit bubble at Skull Kid, he will drop it thus allowing you to go back in time to the first day. The Ocarina of Time has several new songs in Majora's Mask and there are also some of the ones from Zelda 64.
Bombers Notebook - As Link, either play the hide and go seek game or enter the Astral Observatory path using the secret code and talk to the Bombers on the way out. This notebook will allow you to enable various alternate mini-quests that will lead to various items in the game. It will even record the schedules of various characters.
Lens of Truth - If you follow Kapola Gabeola's feathers to the floating cave outside of the Goron Village you will find this item there. It allows you to view hidden or unseen areas. Pretty much the same function as Ocarina of Time.
Land Deeds - These pretty much allow you gain access to occupied Deku Flowers. One can be found in Clock Town, the next in the Southern Swamp, the third in the Mountain Village, and the last in Zora Hall.
Moon's Tear - Can be found by viewing the moon though the telescope at the Astral Observatory. Basically the only function it serves is for trade to get to the Deku Flower in Clock Town.
Bombs - yep you guessed it, they blow up and destroy things around them.
Deku Stick - nothing new here. They can be used as torches.
Bombchus - Nothing new here. They do the same thing they did in Ocarina of Time.
Deku Nuts - they stun enemies if your regular Link, but if you are Deku Link they can be dropped like bombs while you are flying around.
Adult Wallet - if you save 200 or more Rupees at the bank in West Clock Town, the banker will give you this item to carry more Rupees.
Giant's Wallet - If you obtain all 30 Gold Skulltula Tokens in Oceanside Spider House on the first day you will get this one.
Big Quiver - If you schore 40 or more in the Clock Town Shooting Gallery or if you get a perfect score in the Swamp Road Shooting Gallery you will be rewarded with this that will increase your maximum Arrow capacity.
Biggest Quiver - If you score 40 or more points at the Clock Town Shooting Gallery and already have the quiver before this one, you will get the next incremental addition to your Arrow capacity.