Whether a pokemon's design or the stats or some other reason...some Pokemon are so painful to think about being canon that your best course of action is to have selective amnesia.
Now to keep from nitpicking on the same pokemon from a certain generation over and over, I strongly suggest you pick one pokemon per generation.
With 649 pokemon as of right now to choose from (6th generation list not available yet), anyone with says "I can do no such thing!" to this request is a LIAR!
Here's my picks:
1st generation: Jynx (It's creepy! Especially now with purple skin...ewww...)
2nd generation: Politoed (Pointless evolution...and not that great for battles either.)
3rd generation: Armaldo (Anorith is so cute and they ruined it by making it evolve!!)
4th generation: Mamoswine (Why did they have to give it eyes? If it had shaggy hair, I would have loved it!)
5th generation: Garbodor (for literally being garbage!)
So who are your "black sheeps" of the pokemon world and why?
Like the sprites you see here?
Want a custom one of your very own?
Mr. Mime: This is a forgettable Pokemon, literally, since I could only get it through a trade in an obscure building in RBY. Mimey didn't gain an evolution like Electabuzz and Lickitung, which are very close to being my black sheeps. Mimey gained an ugly baby form that retains the mister/junior joke that doesn't even make sense anymore because of genders.
Unown: Learns one attack and has worthless stats. I can't believe I caught the entire alphabet, nicknamed them all because that's what I did in Gold, and earned access to printing more Unown. I cannot and will not print anything from my Gameboy.
Barboach: I forget this for one simple reason. It beat my Latias in the Master Cute Contest. THIS. WORM. IS. NOT. CUTE.
Wormadam: I like Burmy's concept, but Mothim is the sole evolution in my mind. Burmy didn't need a split evolution into a bigger, female bagworm. I know female bagworm don't develop wings but, whyyy? Put Wormadam Pokemon out of its misery, lol. Male Combee give Vespiquen its novelty value... Female Burmy just bother me.
Druddigon: I like all dragons except for this one. It's body structure reminds me of Lego blocks. I always chose Deino over it anyways.
Kangaskhan. I like to pretend like it's not in the Safari Zone because I always have the overwhelming urge to find and catch one even though my luck is shoddy. It's not worth putting that much effort into trying to catch something that doesn't evolve and requires me to waste TMs in order for it to have decent moves.
Qwilfish. Did you even remember that Qwilfish exists? I didn't. Water/Poison, so it's tossed in with the other useless Poison types. Its only use is as a water-based HM slave, but 99% of Water Pokemon fill that role so why bother with this?
Carvanha and Sharpedo. Sharpedo was one of the first 3rd gen designs released and it looked so cool, but then the actual game's release showed that you'd have to evolve this stupid pointed fish to get it and it had no moves. Sure, you could catch one without having to evolve Carvanha, but if you wanted a complete Pokedex then you'd need a Carvanha anyway. Sharpedo's stats are okay, but its defenses are terrible and it's weak to Mach Punch.
Mothim. It was the product of having a male Burmy and there was no point in getting one because Burmy's whole deal was it had different appearances and Mothim was the exact same no matter what Cloak you had. It's kind of like if male Combees evolved into something uglier than Vespiquen. Vespiquen's not ugly, by the way. Muk is ugly.
Heatmor. Nice Special Attack, bad Speed, bad defenses, bad moves, bad typing, bad abilities. This is the pinnacle of uselessness, the ultimate example of bad Pokemon, the very definition of crap.