What Amiibos can be used and what are their effects?

I found a post that gives you a rundown of what amiibos are compatible and what they do.

Here's the rundown from the site (Note all of the descriptions are directly from the source):

Guardian:

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Random Selection of Ancient Materials, such as Gears, Screws, Shafts and Springs.

Bokoblin:

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and a Random Selection of Meat and Weapons.

Toon Link:

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and Random selection of Fish.

8-Bit Link:

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and a Random Number of Arrows and Barrels Containing Rupees.

Link (Archer):

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and Random selection of Meat, Fish, Bows and Arrows.

Toon Zelda:

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and a Random Selection of Herbs and Flowers.

Zelda:

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and Random selection of Plants and Shields.

Link (Rider):

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and a Random Selection of Mushrooms, Weapons and Bridles or Saddles.

Wolf Link:

This Zelda Breath of the Wild Amiibo will summon a Wolf Link Companion to accompany Link. Its maximum heart capacity is based on information transferred from Twilight Princess HD.

Link:

This Zelda Breath of the Wild Amiibo will Unlock a Treasure Chest filled with a Rare Item and a Random Selection of Meat Pieces.

As Timmy Jim mentioned you are able to scan any amiibo but they give you random items not a pre-defined set of items like the Legend of Zelda amiibos.

Source: Amiibo Item Unlocks

I just bought some but haven't tested them all, still I can tell you for those I know :

• Link wolf : as you said it summons a wolf who fight with you

• Link from Smash Bros : first time you use it, it will invoke Epona (so be sure to be near a stable when done, she will only appear the first time and if you are at the beginning of the game when you use the amiibo, place where there isn't any stable to register her, she will be definitely lost !)

• The gardian : it will give you a weapon useful to kill gardians

Those are the ones I find the most useful, but here are others :

• Cartoon link : random fish
• Cartoon zelda / Zelda : random plants
• Link Ocarina : random meat
• Rider Link : a special sword and saddle
• Zelda Botw :a fancy Hylian shield
• Link with a bow : a special bow
• 8 bit Link : random barrels with sometimes money inside
• Bokoblin : some rare weapons

As said by @Timmy Jim in another answer, Non Zelda Amiibo will give you random stuff.

I still have some to test, and things to add as said here but will add it later, as those are the things I remember.

A complete Amiibo list can be found here. To quote:

• Breath of the Wild Archer Link: Drops rare bow-type weapons, plus food and other materials.
• Breath of the Wild Horse Rider Link: Drops a unique horse saddle and food, plus the chance for high-end weapons.
• Breath of the Wild Zelda: Drops a chest containing the Hylian Shield, a very rare item and the best shield in the game. Also drops plants for you to cook with.
• Breath of the Wild Guardian: Drops a chest containing rare weapons and items – including the chance for ancient arrows, super-powerful arrows. Also food.
• Breath of the Wild Bokoblin: Drops a chest containing high-power club-type weapons plus meat to cook with.
• Super Smash Bros Link: The first time you scan it you get Epona, Link’s horse from Ocarina of Time. On subsequent scans you’ll get a selection of food items and a chest that’ll either contain a piece of Twilight Princess Link’s costume (as seen in the video above) or a random piece of weaponry.
• Twilight Princess Wolf Link: This amiibo spawns Wolf link as an ally – he’ll fight alongside you in combat. How many hearts he has is determined by data saved to the wolf in Twilight Princess HD for Wii U.
• 8-Bit Link: The 30th anniversary 8-bit Link amiibo spawns a bunch of barrels. Smash them for food and rupees. He’ll also drop a chest containing a piece of the classic Link tunic or weapons.
• Ocarina of Time Link: Scanning this ridiculously iconic version of Link will drop a bunch of raw meat for you, plus a chest which will either contain a piece of the OOT-era Link costume, the biggoron sword, or other basic weapons.
• Wind Waker Link: Either the Smash Bros ‘Toon Link’ or official Wind Waker amiibo will work for this. Both drop a bunch of fish plus a chest that will contain either a piece of the Wind Waker armor, the sea-breeze boomerang, or other gear.
• Wind Waker Zelda: The 30th anniversary Wind Waker Zelda amiibo will drop a bunch of plants for cooking, plus a chest containing a shield – if you’re lucky, the Hero’s Shield from Wind Waker.
• Smash Bros Zelda / Shiek: Like the Wind Waker Zelda, the Smash Bros. Zelda and Shiek amiibo both drop a bunch of materials for cooking and crafting plus a chest that can contain rare weapons or if you’re lucky the Shiek’s Mask armor from Shiek and the Twilight Bow from Zelda.
• Smash Bros Ganondorf: Ganondorf’s amiibo doesn’t have the nefarious impact he had in Twilight Princess HD- instead he just drops a bunch of materials for cooking and crafting plus a chest that can contain rare weapons – the rarest of which is the amiibo-exclusive sword of the six sages.
• All non-Zelda franchise amiibo: Any amiibo that aren’t of a Legend of Zelda series character will still scan into Breath of the Wild just fine – but instead of giving you specific items, each amiibo will drop a random selection of materials including foodstuff, random loot, or even the occasional gemstone. Every single amiibo on the market is compatible with Breath of the Wild in this way, even the Animal Crossing amiibo trading cards.