Any time there's a wolf or werewolf character you control in a video game, it is instantly my favorite unless the game is utter crap. That being said, in my very first project, which I lovingly named Mountain Story, one of the main characters is a wolf named Argo. While he speaks as well as any Human, due to him being a Guardian to a goddess, he has his own characterization and place in the overall theme and story of the game.
That being said, his primary purpose is as a sort of balance between the other characters, and the first mage of the group. The main character, Marco, is purely melee oriented without any magic in him due to not learning how to tap into it. Argo, while he uses magic, does have melee abilities that allow him to attack multiple times, as well as some more rogueish moves such as howling to demoralize enemies and strengthen his team. Storyline-wise, he is the keeper and protector of the shaman, Terra, who is purely magic-oriented. Terra is a Human raised by wolves, and thus can speak wolf. They use more healing magic than Argo due to their role as a spiritual healer. Another member, Grantz, is the rogue, and is purely more for debuffs and subverting the enemy. A fourth character, who is kind of a spoiler character, acts like the black to Terra's white. Argo is their balance, taking on any role as the battle needs.
Storyline-wise, he's also the fettered, bound by his duty to the Goddess Amaranth, and serves as the Mr. Exposition of the group regarding anything spiritual or relating to deities or Hellions. This is reflected in how, barring certain instances, he never changes, or is able to change, his equipment because it is bound to him by oath to Amaranth.
All of that aside, there are other instances of wolf or wolflike characters in my games. They all act as a natural counterpart to most characters' divide with nature, In and out of combat, they're loyal and help their allies more than themselves and rarely do well by themselves. They often serve as an aid to other characters, and can streamline an attack so that one or more characters can attack together for massive damage. One thing I want to implement with wolf characters is a single-character multi-tech system, similar to Chrono Trigger, where the wolf and other characters attack simultaneously, with an ultimate tech being all of them attacking or casting a spell or what-have-you for a 100% accurate attack. (Which would bypass certain immunities, which would be handy for a boss.) Sadly, I haven't found a reliable method of doing this yet. Feel free to use that particular idea, and if my words have inspire you, well thank you, it feels nice to inspire people. :3