You can scan each Amiibo once per day. A few of them have rare items. Each time, you have a random chance of the Amiibo dropping it's rare item. Note: Epona is guaranteed to drop the first time you scan SSB Link, but it only ever happen once per save game. You should only summon Epona if you have access to a Stable to keep her permanently.

Unlockable	How to unlock
Biggorron's Sword	30th Anniversary Ocarina of Time Link
Epona	Super Smash Bros Link and Twilight Princess Link (1st Time always, randomly after if she is lost)
Fierce Deity (Armor Set)	Majora's Mask Link
Fierce Deity Sword	Majora's Mask Link
Goddess Sword	Skyward Sword Link
Hero's Shield	30th Anniversary Wind Waker Zelda
Sea-Breeze Boomerang	30th Anniversary Wind Waker Link or Super Smash Bros Toon Link
Sheik's Mask	Super Smash Bros Sheik
Sword	30th Anniversary 8-bit Link
Sword of the Six Sages	Super Smash Bros Ganondorf
Traveler's Saddle and Bridle	Breath of the Wild Rider Link
Tunic of the Hero (Armor Set)	30th Anniversary 8-bit Link
Tunic of the Sky (Armor Set)	Skyward Sword Link
Tunic of the Wind (Armor Set)	30th Anniversary Wind Waker Link or Super Smash Bros Toon Link
Tunic of Time (Armor Set)	30th Anniversary Ocarina of Time Link
Tunic of Twilight (Armor Set)	Super Smash Bros Link and Twilight Princess Link (2nd Time and Beyond)
Twilight Bow	Super Smash Bros Zelda
Vah Medoh Divine Helm	Champion Revali
Vah Naboris Divine Helm	Champion Urbosa
Vah Rudania Divine Helm	Champion Daruk
Vah Ruta Divine Helm	Champion Mipha