Sunflora. And it is worse until you find a Sun Stone.
Unown. It was only made for the gimmick of the Pokemon alphabet and it can only know Hidden Power, which, come to think of it, I don't even use.
I would have said Shedinja too, but once you know how to manage the Wonder Guard ability and making it learn X-Scissor and Shadow Sneak, it's actually quite decent and one of my favourites. :D
Delibird for being trolled. It has both Vital Spirit and Insomnia.
To clarify on the last point, Magikarp takes forever to train and does practically nothing (maybe Tackle also) until it finally reaches Gyarados, which makes it almost worth it.
Meanwhile, Metapod on the other hand, is only not as bad if you train it from a Caterpie. I caught a Caterpie in Yellow, and once it became a Metapod, it still knew Tackle and String Shot (a wild Metapod would not know these). After it became a Butterfree a few levels later, it could use Confusion, which came in handy, as it was an extremely powerful move for my team.
Anyway, I believe the most useless would have to be Ledian. 4x Weak to Rock, Stealth Rock murders it, it has such a low defense, and it can't hit anything.
Current Pokemon Black Team:
Always challenge yourself in Pokemon. The toughest Pokemon make the game too easy.