Read-only feature:

Bring Wolf Link into the game as a partner character

It will retain any hearts earned in Twilight Princess HD (Wii U). Else it will default to three hearts of health.

Read-only feature:

Bring Epona into the game as a rideable horse

Read-only feature:

Receive materials and a rare or exclusive item

Once a day per amiibo.

Some items can only be obtained from amiibo. Those are (following the amiibo that can drop them):

Link - The Legend of Zelda (8-bit): Cap/Tunic/Trousers of the Hero, Sword
Link - Ocarina of Time: Cap/Tunic/Trousers of Time, Biggoron's Sword
Link - Majora's Mask: Fierce Deity Mask/Armor/Boots, Fierce Deity Sword
Toon Link (Super Smash Bros.) or Toon Link - Wind Waker: Cap/Tunic/Trousers of the Wind, Seabreeze Boomerang
Link (Super Smash Bros.) or Link - Twilight Princess: Cap/Tunic/Trousers of Twilight
Link - Skyward Sword: Cap/Tunic/Trousers of the Sky, Goddess Sword
Link - Rider: Traveler's Bridle/Saddle
Sheik: Sheik's Mask
Ganondorf: Sword of the Six Sages
Zelda - Wind Waker: Hero's Shield
Zelda (Super Smash Bros.): Twilight Bow
Mipha: Vah Ruta Divine Helm
Revali: Vah Medoh Divine Helm
Urbosa: Vah Naboris Divine Helm
Daruk: Vah Rudania Divine Helm

Any other amiibo listed below, like Young Link (Super Smash Bros.) and Link - Link's Awakening, will drop materials and weapons but no amiibo-exclusive items.

Source: Zelda Wiki / Thanks: Boblers, memoryman3

Read-only feature:

Receive materials

Once a day per amiibo

This feature works with any amiibo (with the possible exception of those that work with its other features).