The Breath of the Wild Zelda amiibo has a particularly useful effect — when you tap her, there's a chance she'll drop a chest which contains a Hylian Shield. Like most special items, there's not guarantee, but there's a possibility she can drop this. The Hylian Shield is by far and away the best shield in the game, and is only found out in the wild in one location, deep within Hyrule Castle. If you don't have this amiibo, we've got a guide to getting that naturally. She also drops food items.
The Archer Link amiibo for Breath of the Wild drops random food items plus a chest that has a chance of containing a powerful bow.
The Horse Rider Link amiibo for Breath of the Wild drops random food items, but also has the chance to drop powerful swords or special saddles for your in-game steed.
The Guardian amiibo is cool as hell to look at. It drops rare food items and also has a chance of dropping strong weapons and ancient arrows, the rare arrows that can one-shot these powerful enemies with ease.
The Bokoblin enemy amiibo from Breath of the Wild will drop random food and elixir items for you, but also has a chance to drop powerful club-type weapons for you.