In SAELIG there are a number of pets you can get. Pets don't have a huge function in the game, but they do offer some added roleplaying potential and they're cute. You can also pat them and feed them. Pets have a lifespan and will end up dying, so be prepared for that.
You can have a max of 5 pets at any one time.
Lifespan: 15 years
Likes: Meat, fish, pats
Cats are obtained through production events when you own certain businesses that attract rats. When the event happens you can choose to abandon the cat, adopt it as a pet, or hire it as a rodent catcher. When hired as a rodent catcher, it will keep all rats away from your business so you will no longer have any negative rodent based production events.
Lifespan: 10 years
Likes: Meat, fish, eggs, pats
Dislikes: Cold winter nights without a warm fire to snuggle up near
Foxes can be befriended when you are out hunting and you tend to find them as cubs after you have killed another fox (usually its mother). Once the cub is found you will have the option to adopt or abandon.
Lifespan: 5 years
Likes: Wheat, barley, oats, pats (I guess)
Dislikes: Eggs that are too big for it
Pet chickens can be found by foraging through the town coops. The more time you spend at the coops, the more likely it is that one of the chickens will take an intense liking to you and begin to follow you around. You'll be able to adopt it as a pet, or ignore it.
Lifespan: 18 years
Horses are bought from a travelling horse breeder who will sometimes show up in town. Horses can be mounted by your player and used as transport. When not being ridden horses will follow you around like any other pet.