BIONICLE: Matoran actually have Required Secondary Powers, but have a minuscule amount of Elemental Powers. Of course, when they do become Toa, they will have the necessary secondary power for their element.
Mixels shows off some characters that actually lack these powers, and end up affecting their own abilities thanks to this:
Lunk and Slumbo, being ice-based Mixels, have a low base temperature and live in a frozen wasteland. As a result, they are both horribly slow and lethargic.
Balk uses his head like a rubber mallet to defend himself. Unfortunately, this does not translate to the inside of his head, and he has brain damage as a result.
Chomly is a living trash compacter that eats anything he can find and his mouth is not made for chewing properly. One of his upper teeth is now replaced with a gold one.