Gen 1: Mafia boss
Gen 2: None, decapitated criminal organization
Gen 3: Nerd and beefcake ecoterrorists
Gen 4: That guy from Linking Park?
Gen 5: PETA, literal white knights, and cinnamon roll
Gen 6: Obviously evil guy. What he and his group did to fashion is a crime worse that the one he was trying to commit in the first place
Gen 7: THE ABSOLUTE MADMAN!

RGBY/FrLg: Mafia, lead by the boss
GSC: Broken mafia, lead by faceless mafia interim
HGSS: Broken mafia, lead by four mafia interims with faces
RSE: Hoodie and sailor thugs, lead by ecoterrorists
ORAS: Hoodie army and pirate thugs, lead by nerd and beefcake ecoterrorists
DPPt: Bowlcut Romulans, lead by Evil Spock
BW: PETA white knight cultists, lead by genre-savvy psychopath and his autistic son
B2W2: Ninja robot pirates, lead by genre-savvy psychopath
XY: Insufferable fashionistas, lead by furiously bearded apocalyptic extremist
SM: Anarchist pirate gang, lead by a crazy motherfucker

And as a bonus:
Colo: Unsuspecting rotund mayor who is actually very athletic
XD: Unsuspecting kindly old man who is actually very athletic