There's that kid in Wind Waker with the giant snot trail coming out of his nose. I'm not sure if he's anybody's favorite.
Your "friends" at the start of Secret of Mana ditch you and help get you banished from your hometown. Practically speaking, they've got to be some of the worst.
Personally, I don't think there's an abundance of good "interesting" examples like Oliver, because children in games usually have small roles and they have a narrow range of narrative development/plot involvement. Or if they are the main characters, then they occupy very straightforward protagonist roles.
Rydia from FF4 is one good one, probably the one of the most compelling child protagonists in an RPG. She starts out being profoundly affected by her mother's death and an associated fear of fire, and throughout the story she grows up and turns around to be the one to save Cecil from his biggest enemy. A very elegantly told character arc given how it use gameplay mechanics and plot related events to tell her story, rather than just dump a bunch of text and loyalty missions on you.
One child character that I'm fond of is 'Teddy' from Actraiser. Despite being a small boy (I think), he tries to solve the mystery of the blood red lake on his own. As God, your charming role in this sequence is to accept his worried mother's loaf of bread, and then leave the bread for Teddy to find so that he might get homesick and return home. Teddy is also involved in being one of the unfortunate townspeople randomly chosen to be sacrificed to the region's monster (before you intervene, of course). In the Japanese version, you learn much later during the credits that Teddy had rigged the random selection so he would get one of the short straws. Quintet is the master of small vignettes, and this one echoes the importance of home and being eager to take on responsibility for your family/tribe.