Pokemon (non-NFE) with the LEAST competitive value.

Farfetch'd has pretty bad stats, a total base of 352 and it has a terrible movepool. Still going to use one on a mono-normal team for the E4 in Black 2, in-game with enough training it will probably be suitable enough, pretty much all Pokémon are, but yeah, I can't see it being anything but the shits competitively.

 

I'm surprised Luvdisc hasn't been said yet.
Horrible movepool backed by horrible stats (except Speed) and with the ability Swift Swim (but why use THIS thing over Kingdra or Kabutops?) At least Basculin gets Adaptability and decent stats to pull it off (though there's Crawdaunt who is a better candidate) so I don't think it's all that useless. I do agree Farfetch'd is pretty bad too as there are so many options to consider over it (like Swellow, Braviary, etc)
Also Unown, only Hidden Power and crummy stats; what a gimmicky Pokémon...

 

Bidoof would've been mentioned here if not for Moody Dunsparce is pretty bad.

 

Like Scrafty said, Unown. Seriously why was this thing ever made?