What is preserved when playing the Song of Time?

In The Legend of Zelda: Majora's Mask, gameplay spans three in-game days; however, completing everything necessary within just those three days is impossible, and so one must regularly play the Song of Time to time-travel back to the beginning of the three-day cycle. In doing so, some progress is kept, but many other things are reset.

What is kept and what is lost when using the Song of Time to return to the beginning of the three-day cycle?

Solution 1:

(Note: The following answer is based on the 3DS remake, with Zelda Wiki consulted for any changes from the N64 version, so if any of this is wrong in the original game, blame the wiki.)

The following things are kept when playing the Song of Time:

• Heart Containers and Pieces of Heart
• amount of health and magic remaining
• Masks and boss remains
• Ocarina songs (other than the Scarecrow's Song)
• the Bombers' Notebook and entries therein
• the Pictograph Box (but any photos taken are not kept)
• rupees deposited with the Banker
• the Hero's Bow, acquired arrow types (Fire Arrow etc.), and quiver upgrades (but actual arrows are not kept)
• Bomb Bag and its upgrades (but bombs are not kept)
• Bottles (but not their contents)
• Kokiri Sword
• Gilded Sword
• Hero's Shield
  • If the Hero's Shield has been swallowed by a Like Like, you will still be shieldless after playing the Song of Time
• Mirror Shield
• Lens of Truth
• Hookshot
• rewards from reassembling Stray Fairies into Great Fairies
• activated Owl Statues
• maps purchased from Tingle
• wallet upgrades
• Powder Keg certification
• dungeon maps and compasses
• Lottery Shop winning numbers

The following things are lost or reset when starting a new cycle:

• All dungeon bosses will be alive again, and the negative environmental effects on their areas will be present again
  • The game does remember which bosses were previously defeated (or, in the 3DS remake, previously fought), allowing you to warp from the dungeon entrances right to the boss battles for rematches.
• Progress in sidequests is reset
  • If a sidequest gave a reward of a Piece of Heart, mask, or other item preserved across cycles, the reward will be kept. If such a sidequest is then completed a second time, the reward will be either rupees or (in the 3DS remake) a Fishing Hole Pass.
• Sidequest-specific items are lost:
  • Moon's Tear
  • Title Deeds
  • Stock Pot Inn Room Key
  • Kafei & Anju sidequest items (Letter to Kafei, Pendant of Memories, and Special Delivery to Mama)
  • Mystery Milk/Moldy Milk (3DS remake)
• The Scarecrow's Song is unset
• The Razor Sword degrades back to the Kokiri Sword
• If the sword is being upgraded at the Mountain Smithy, you will get the Kokiri Sword back
• Any rupees in your wallet are lost
• All "stacked" items (deku nuts, deku sticks, arrows, bombs, bombchus, magic beans, powder kegs) are lost
• Contents of Bottles are lost
• Opened treasure chests will be closed and filled again (Opened treasure chests containing Pieces of Heart will afterwards contain rupees)
• Any magic beans planted will be gone
• Items stolen by the Takkuri are regained
• General dungeon progress is reset
  • Small Keys and Boss Keys are lost
  • Stray Fairies gathered in dungeons are lost (though any previously gathered will be marked on the map in future cycles), and the corresponding Great Fairies revert to shattered form
• Any photos taken with the Pictograph Box are lost