When sequence breaking, it becomes important to understand what actions trigger certain events or item drops.
Note that beating a dungeon means touching the blue warp and either watching the cutscene after, or skipping it while still obtaining the stone/medallion.
event - trigger
Get arrow drops - Item in bow slot
Get bomb drops - Item in bomb slot
Buying arrows - A non-zero Quiver in inventory
Buying bombs from Bazaar and Deku Scrubs - Goron Ruby and a non-zero Bomb Bag in inventory
Buying bombs from Goron Shop as Adult - Goron Ruby and a non-zero Bomb Bag in inventory
Buying bombs from Goron Shop as Child - Beat DC, Goron Ruby, and a non-zero Bomb Bag in inventory
Buying Goron/Zora Tunic - Be Adult
Bombchu Bowling open - Beat DC
Bombchu Shop open - Beat DC
Gerudo Archery game playable - Item in Bow slot, Gerudo Card, Epona
Kakariko Archery Quiver Upgrade Reward - Quiver 30 or 40 in inventory
Get weird egg - Enter Hyrule Castle (outdoors area) and reload the area
Remove Mido from Deku entrance - Met Zelda and received Letter
Saria in SFM - Met Zelda and received Zelda's Letter (Lullaby is not required, but Zelda's Letter will be reverted to Chicken if you savewarp without Lullaby)
Happy Mask Shop open - Showed Zelda's Letter to the guard in Kakariko
Epona's Song available - Wake up Talon as child and talk to him
Lon Lon Ranch Cucco collecting game - Woke Talon as child and talked to him
Running Man in field - 3 Spiritual Stones in inventory
Zelda Escape Cutscene (for Ocarina of Time) - 3 Spiritual Stones in inventory
Open the door of time - Enter Temple of Time from outside the temple and Play Song of Time
Nocturne Cutscene - Beat Forest, Fire, and Water Temples, and enter Kakariko from Hyrule Field
Prelude Cutscene - Beat Forest Temple
Able to drop master sword - Beat forest and Prelude Cutscene
Light Arrow Cutscene - Shadow and Spirit Medallions
Rainbow bridge - Shadow Medallion, Spirit Medallion, and Light Arrow in inventory
Lake Hylia Water Rises - Beat Water Temple and watch the cutscene
Owl in Lost Woods near Goron City warp - Zelda's Lullaby in inventory
Owl in Lost Woods near SFM - Saria's Song in inventory
Owl in front of Kakariko gone - Zelda's Lullaby in inventory
Owl in Zora's river appears - Met Zelda and received Letter
Owl in Zora's river disappears - Played Zelda's Lullaby to the Sleepless Waterfall in Zora's River
Owl in Hyrule Field near Gerudo Valley disappears - 3 Spiritual Stones in inventory
Owl in Hyrule Field near Lake Hylia disappears - 3 Spiritual Stones in inventory
Owl in DMT will give you a ride down Death Mountain - Have Magic meter