DK 64 might count. There isn't much characterization in the game, but I think he's one of the weakest characters, and he has to use his skills more instead of doing action-y things. And he's based on an orangutan.
Fallout looks like it counts too:
Ian is the first companion you're likely to get, and his personality contrasts the protagonist (he's an experienced Wastelander, you're fresh from the vault)
Then later on you can recruit fighter-guy Tycho (high strength, low intelligence), sneaky-girl Katja (low strength, high intelligence), and, at some point, Tandi will get kidnapped and you'll have to rescue her, and she's useless.
It seems obvious that when all the possible companions were being thought up, they ended up falling into this trope.
edited 31st Jul '12 1:27:36 PM by abk0100