“Favorite animal sidekick, pet, or summoning from any anime”
Right off the bat I’m going to say that, despite many of them looking like animals and originating as a virtual pet like Tamagotchi, Digimon don’t count. Partner Digimon in the anime interact with their human partners like other people, not like pets. Sometimes even specific human relationships; Agumon is like Masaru/Marcus’s henchman, Ikuto/Keenan calls Falcomon his brother, and in one yuritastic moment Renamon compares her relationship with Ruki/Rika to Jijimon and Babamon’s marriage.
But I can’t think of a reason why Pokemon shouldn’t count, and considering the nature of the show it seems entirely reasonable that they could actually be some of the better developed “pet” characters around…though some of them aren’t.
My favorite ‘pet’/animal in anime is the Pokemon that started off as Paul’s Chimchar
and wound up as Ash’s Infernape.
little big monkey has a hidden power, a souped-up version of the normal Blaze ability, and Paul had a habit of being really rough on it to bring it out. When that didn’t work out so well Paul released Chimchar for being “useless”. Ash immediately invited Chimchar to join him instead, and predictably, but satisfyingly, Ash eventually won a battle against Paul thanks to Infernape.
For more traditional examples, I guess I’ll mention Ryo-Ohki the cabbit from Tenchi Muyo!