Companions

Companions are gear that can only be received through chests, with the exception of Wolves, which can be found while using the Bone Pickaxe. All companions increase your base PPS, and here is an equal chance to receive each Companion. There is an equal chance to receive each companion.

Before update 2.14
Prior to the 2.14 updates, companions could also be received by purchasing them in the gear menu. The companion that was available for purchase was random with a random price in a range based on the material.

Prices of 20, 30, 40, 50, 60, 70, or 80
Pumpkin, Glass, Gold, Diamond, Emerald, End Stone, Ruby, Topaz, Jade, Prismarine, Pearl, and Alien Ooze

Prices of 200, 300, 400, 500, 600, 700, or 800
Dirt, Wood, Clay, Sand, Sandstone, Cactus, Ice, Snow, Gravel, Stone, Coal, Iron, Redstone, Lapis Lazuli, Bedrock, Obsidian, Netherrack, Soul Sand, Nether Brick, Nether Quartz, Glowstone Dust, Red Sand, Red Sandstone, Hardened Clay, Orchid Seeds, Coffee Beans, Dandelion Seeds, Jungle Log, Podzol, Sponge, Coral, Live Rock, Moon Rock, Aluminum, and Diorite

Not Tradable
Winter Candy (outside of Winter Event), Tumbleweed, Starfish Shards, Lunar Meteorite, Asteroid Shards, Cheese, Gunpowder, and Runic

Trivia

 * Most Blocks in the 20 - 80 range of prices are rare. Bedrock, however, is not within that range, making it a common obstacle when amassing companions.
 * Most of the untradable items are unique by either only being available during events, not obtainable from a block, or extremely rare. Lunar Meteorite does not possess any of those properties, so its reason for not being tradable is unknown.