2.) The Walking Dead
Another type of character aside from animals that will surely pull your heartstrings would have to be children. In Telltale's The Walking Dead, we follow Lee and a young girl under his care named Clementine. Throughout the game, you grow a bond with her and develop a sense of responsibility towards taking care of her.
There were a lot of heart-wrenching moments in the game, but the end breaks your heart to little pieces. Lee gets bitten and players have the choice to let Clementine leave him to turn or shoot him before it happens. I chose the latter to end his misery, but I ended up an emotional wreck after.