Just Here for Godzilla: A textbook example. The main human cast is largely interchangeable with the typical Hanna-Barbera cast, and fans generally hate Godzooky, but the battles between Godzilla and the other monsters can still make up for it.
The Scrappy: Godzooky. He gets a lot of hate from the Kaiju community, though in his defense, he's just a baby monster and may mature into something bigger and more likable if the series ever gets rebooted.
They Wasted a Perfectly Good Plot: As unloved as he is, Godzooky actually could have been the basis for a promising storyline. He's canonically said to be Godzilla's nephew—and unless the Big G is merely his Honorary Uncle, this would presumably mean that Godzilla also has at least one sibling. But for some reason, this idea was never explored, and Godzooky's parentage is unknown.
Well, technically, the original Godzilla did die in the original movie. Maybe Zooky is his kid.