Captain Planet - Based on Ted Turner's environmentally pandering superhero show (which I used to watch because it was the only thing on during early Saturday mornings). My brother and I rented this from the local drugstore, and weren't quite sure what to do. You play some stages in a plane and others as the Captain himself, and you can switch between the five elemental powers. We could never figure out exactly what some of the powers did, however. In the plane stages, Heart was just as useless as you would expect it to be.
Taz-Mania - In this Super NES game, the Tasmanian Devil runs around a racetrack eating kiwis, which then inexplicably pop back out of his mouth at the end of the level, making the whole thing a rather futile exercise to my mind. Even putting everything else aside, what about the cartoon suggested that a racetrack game would be a good idea? Did they just have this engine lying around from an unused racing game, and then said, "Eh, what the hell, let's just throw Taz into it"? I understand that the Genesis game based around this property is a more traditional side-scroller.
Where's Waldo? - Far be it from me to condemn a game based solely on graphics, but if the object is to locate something in a picture, shouldn't you be able to tell what you're looking at? There was another part to this game besides the traditional Waldo-finding, but when my brother borrowed this game sans instructions, I don't think he could figure out what you were actually supposed to do in that part.
Barney - I've never played this or seen it played, but bethje said she tried it once, and there's a part where Barney rides on a cloud. If you try to make him step off into the bottomless void beneath, he'll just say something like, "It's not time yet!" So the pleasure that I'm sure a great many gamers would get out of killing Barney is denied them.
Journey Escape - An Atari game Beth has, where you have to guide the members of the band Journey to a spaceship, while avoiding the crazed fans. You can become invincible when you touch something that looks like the Kool-Aid Man. I'm sure there are more games based on bands, but I can't think of any offhand. I remember reading about a Duran Duran board game, but I don't think they ever made the leap into the world of video games.
Cool Spot - Based around the short-lived 7-Up mascot, I don't remember this game being particularly bad, but I think games based around advertising campaigns are just kind of weird. I was trying to think of other commercial characters who had their own games, and McKids and Yo! Noid (neither of which I've actually seen first-hand) came to mind. There are also those Xbox games that Burger King recently sold featuring their own mascot, and I seem to recall hearing about games starring Chester Cheetah and the aforementioned Kool-Aid Man. Can anyone think of more?