A recent Nintendo Direct revealed how connecting a Link Amiibo with Hyrule Warriors would unlock an in-game weapon for Link, the Spinner from The Legend of Zelda: Twilight Princess.
It has now been confirmed that the Toon Link Amiibo will also unlocked the Spinner.
All other Amiibo figures are compatible with Hyrule Warriors, each of them unlocking various materials or rupees.
The Japanese Amiibo site lists Hyrule Warriors are being compatible with "all other Amiibo" but specifically calls out Link, Toon Link, Sheik, and Zelda, though it doesn't say whether the Sheik and Zelda Amiibo will have a more special effect. Stay tuned for further developments.