Your company can keep four kinds of animal. Each comes from a vanilla animal you tame: sneak and right-click it with an empty hand to open the taming menu. They are drawn with the vanilla textures.

Guard Dog

• How to get: sneak + right-click a wild wolf with an empty hand: the taming menu; costs one raw meat. Pick the hireling it goes with (a Town Guard or Hunter) or no one. Town Guards also tame wild wolves themselves with raw meat (1 in 3 chance per try) until they have two dogs; wolves within 64 blocks of their post.
• Behaviour: goes with its guard or hunter (keeps within 4 blocks, runs to catch up beyond that, teleports past 64), fights monsters within 16 blocks of its guard (never creepers) and anything that hurts them, or keeps watch over a guard spot (ranges 8, 12, 16, 24, 32; default 12), or waits at home (its Dog House, else by its bowls) and sees off monsters within 8 blocks. Hunters take it on their trips.
• Food and water: both run from 100 to 0 over a day (100/1200 per second); below 40 it goes to the nearest Feed Bowl / Water Bowl (within 16 blocks, or the company's nearest within 256). Hungry or thirsty, it stops guarding. Fed and watered, it heals half a heart a second, 5 seconds after last hurt. Two dogs per Dog House.
• Settings: the Crew Board's Animals page (who it goes with, guard spot and range, recall, wolf armor slot).

Cat

• How to get: sneak + right-click a cat with an empty hand; costs a raw cod or salmon.
• Behaviour: creepers keep away from it and phantoms from the ground round it, as from any cat; it sees off rabbits (crop pests), silverfish and endermites round its spot (its guard-spot range, round its leader, or within 10 blocks at home). Goes with whoever recalled it, keeps watch over a spot, or waits where it was tamed.

Pack Donkey

• How to get: sneak + right-click a donkey with an empty hand; costs a Hay Bale.
• Behaviour: with a Gatherer, Hunter or Herbalist it goes on their trips and comes back with its pack (18 slots) full of extra finds. Otherwise it goes with whoever recalled it, stays at a spot, or waits in a Stable area. Eats Hay Bales and drinks from a Water Trough in a Stable (food and water run down like a dog's). The pack opens from the Crew Board anywhere, or up close. Can be ridden with a saddle.

Horse

• How to get: sneak + right-click a horse with an empty hand; costs a Hay Bale.
• Behaviour: a Courier's horse goes with them and halves delivery time; a Town Guard rides theirs on rounds (gets on within 8 blocks). Otherwise waits in a Stable eating hay and drinking at a trough; Recall brings it to the player to ride (ridden speed modifier 2.0). Saddle and armor are set from its Animals profile.

Picture to add: a Town Guard with two Guard Dogs by a Dog House