Ever since it was moves and not type that determine if attack or special attack is used, it's really hard to point out really terrible Pokemon that aren't just normal types. Gyarados used to be a waste of Pokemon back when it had the high attack growth but all water moves used Special Attack. Still, I can find the evolved Pokemon with the worst stat growths as well as being a horrible type in the first place:
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Normal: #132 Ditto
Bad at speed and every other stat, including health. Sure, its transform will copy the stats over, but half its health will be gone as it'll probably be going second, and then it'll just be the same as the opponent but with less pp for each move.
Bug and Ghost: #292 Shedinja
He's got Wonderguard and that's about it. He will always always have 1 hp (I'm pretty sure) so weather effects can take them out in one turn. Also he can still be damaged by the following types... fire, flying, rock, ghost and dark.
Bug: #313 Volbeat
Volbeat and Illumise are nearly the same, but Volbeat focuses on the Attack stat while featuring a mostly Special Attack moveset. Sure, you can use TMs for more Attack moves, but the attack stat is actually less than Shedinja's.
Psychic: #201 Unknown
All they've got as a move is Hidden Power. Their speed sucks, their hp sucks, their defenses suck. They've only got less-than decent fighting power. But again, all they have is hidden move. Good luck finding one though.
Normal and Flying: #83 Farfetch'd
Stats just marginally better than even Ditto but with the added benefit of having three weaknesses instead of just one. It's higher-level moves include Feint and False Swipe... what a joke.
Ghost and Dark: #302 Sableye
Being the only Pokemon I can think of without weaknesses (if you don't count a fighting pokemon using an ident move). But that's it, the stats are meh across the board. And unlike Wobbuffet, it doesn't have any moves to take advantage of the no weaknesses thing.
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These are my picks for the worst of the worst. Smeargle was a close second to Ditto, but they're both straight normal, so I had to drop one. I can bet though, that with this team, you'd have a hard time beating the league even at level 75+. If you have to find an alternate for Unknown, go with Medicham.
Edit: I made this list with the assumption that you will be evolving your Pokemon. If you aren't, then I can give a whole host of other Pokemon that suck way worse.
