"The ultimate villain of the story, who's causing the problem the heroes must solve."
Note that Big Bad is not a catch-all trope for the biggest and ugliest villain of any given story. The Big Bad is the one who turns out to be behind several other seemingly independent threats.
A Game Of Gods originally had Omega as the Big Bad, who was behind all the disappearing Champions and was possessing a doomsday device. However, after he kicked the bucket, Lambda came in and some Fridge Horror came up, resulting in them going back for Echidna and confronting the true Big Bad, Digamma.
In Greek Ninja, it turns out that the no-match-for-any-human-being force that was so strong it could destroy the whole world, was in fact nothing more than a bitter human being himself, who was purposefully reincarnated simply to get revenge and restore the reign of the Olympians.
Michelle Clore from KateModern is responsible, either directly or indirectly, for nearly everything that goes wrong over the course of the series.
Madness Combat had the Sheriff as its first Big Bad, who got killed relatively quickly, followed by Jebus and eventually the Clown. Then the Auditor showed up and things really hit the fan.
In Mario Brothers, King Koopa is this with his army of troops. He personally kills Luigi and plans to kill the Princess and Mario.
The Mysterious Somebody, Bracket Fungus and League of Mary-Sue Factories take this role for the Protectors of the Plot Continuum. Despite being long dead, the Mysterious Somebody could be said to be the most influential Big Bad, as his actions more or less shaped the PPC's identity in-story; the League is a series of offshoots from his original Mary-Sue Factory, and the organisation of the PPC itself is a reaction to his actions as its head.
Originally it was implied that Ozzie Arcane was the Big Bad of The Quest For Geekdom, but it was eventually revealed to be Eric Rosethorn.
Seasons 9 and 10 are setting up the Director as the villain, particularly for the flashback episodes. The latter also reveals Sigma as the true Big Bad of Reconstruction and the Bigger Bad of Recreation and Revelation.
Seasons 11 and 12 have General Doyle apparently fitting this role except his apparent Dragon, Locus, isn't working him but for the true Big Bad, the mysterious Control.
Danya commands the terrorist organization in charge of Survival of the Fittest, and is therefore primarily responsible for the students being abducted and forced to kill one another, even though as of yet it is unknown if he has ever directly killed anyone. This makes his status as Big Bad inarguable. At least until he's killed by Dorian Pello.
Each Survival of the Fittest Endgame tends to have one major villain from the students too. V1 had Cody Jenson, the killer of Adam Dodd's girlfriend and best friend, V2 had Mariavel Varella, the biggest killer on the island, who further cemented her status when she killed Bryan Calvert's girlfriend, and V3 had J.R. Rizzolo, who actually ended up winning.
Taco Man, in "Taco Man: The Game Master," has certain villians. In "Taco Man Plays A Video Game," however, when he got tired of playing Bubsy, Taco Man had a dream of a evil Bubsy forcing Taco Man to play Bubsy 3D, and then, Taco Man realized it wasn't a dream, because the Bubsy 3D title screen was on Taco Man's TV, and the evil Bubsy forced Taco Man to play Bubsy 3D, and then, after Taco Man was treated to a death animation in Bubsy 3D, the evil Bubsy said that there was Bubsy II and Bubsy for the Jaugar, and the evil Bubsy disappears.
Twitch Plays Pokémon. Yes, the entire "canon" is made up of Ascended Fanon, but surprisingly each instalment so far has had one character whom the Mob basically all agrees to blame for anything bad (Pokémon getting released, countdown timers, etc).
The unseen supervillain Nimbus seems to be behind everything. The superweapons at Halloween, the deviser drug used on Merry and maybe also G-Force, and so on. Even some of the Christmas holiday adventures had Nimbus lurking somewhere behind the scenes. We still don't know what he's up to.
That said, "Seńor X" seems to be responsible for everything that Nimbus isn't. Among other things, he's indirectly responsible for everything Hecate did, and by connection, half the bad stuff the Alphas were up to early on. More importantly though, a recent story revealed that There was a very powerful and very subtle spell active on campus designed to increase tension and conflict, and he's implied to be the one responsible — making him indirectly responsible for the actions of more or less every on-campus bad-guy to date. Oh and it's practically been confirmed by this point that he's masquerading as a student.
In the recent story "Razzle Dazzle", Thomas Townsend, alias Mephisto the Mentalist, alias Cerebrex the Super-Brain, claims to have been scheming against many different heros for over eighty years. Under the alias Dominus, he's the current boss of the Syndicate. We don't know for such how much of this is true, since Thomas Townsend admits that he's an Unreliable Narrator.
Considering how little we know about these Whateley Big Bads, it's possible that two or more of them are the same person.
Worm at first appears to have a Big Bad Ensemble, between the multitudes of supervillains, the three Endbringers, the Slaughterhouse 9, and Cauldron, but the best contender for the role is the Simurgh, the third of the Endbringers, a malevolent, massively powerful telepath and precognitive with a fondness for Disaster Dominoes and brainwashed pawns, who is essentially responsible for the world being in the state that it is by sabotaging any attempts to improve the world almost before they start, and who may be The Man Behind the Man for any of the above.
However, the real Big Bad turns out to be Scion, who spends most of the story looking like the Big Good.