In games like Animal Parade and Tree of Tranquility you can befriend any wild animal up to 6 hearts an take it home. Other games such as Sunshine Islands, you must raise someone's friendship to a certain level before you'll be able to enter a cutscene allowing you to get that pet. Magical Melody is the only one yet that you can unlock a pig. In Tale of Two Towns, Grand Bazaar, and A New Beginning your pets can herd your animals.
In Story of Seasons: Trio of Towns, Hamtaro was accounced as a pet that would be obtainable within the game. Very few details has been announced, but it is known that Kurumi Mamiya, his original voice actor, will be returning for the role.