"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.
Ho-oh in Poké Wars, who is later forcibly replaced by his Evil Genius, Uxie, who is a billion times worse.
The Vizard Trilogy had an interesting variant. Each of the four stories has its own Big Bad, all of whom are part of the Five-Bad Band, but the most involved in the overarching plot is Asayama Shiba. By contrast, her leader, Takeshi Katano, is a Non-Action Big Bad; he's the most powerful of the Five-Bad Band and the leader of the Visoreds, but he barely does anything present-time, apart from sending an underling to save Ami and Rukia after a fight. However, the reason Asayama got so far was because Katano let her continue her machinations.
ATLAR has Zotu and Azul's father, Aizo, set up as the Big Bad in book one, with an expanded role in comparison to the original series' first season, but once Azul is properly introduced, it is clear that she will drive the plot far more-so than her father.
The Big Bad of the Mass Effect fic The Council Era is set up as the Krogan Overlord, Kurvok. In fact, Kurvok is swiftly usurped by his advisor, Halak Marr, and Kurvok is dead by the end of Part One, while Marr is present until the very end of the series.
The Pony POV Series is an interesting example: while Discord is only the direct Big Bad in certain Story Arcs, he's also the Bigger Bad of the series as a whole, as even the arcs where he doesn't show up in person are still all the fallout from his actions in canon and the Back Story and there's also a subplot running through the series about his backup plan to escape his prison again. For the sake of precision, we'll break it down by arc:
Naturally, Discord himself in the original Discorded Ponies series, as it's set during his canon appearance. This also includes the Alternate Ending Epilogue (eventually expanded on in the Dark World arc), which shows what would have happened had he actually managed to win.
The Reharmonization arc has Loneliness — maybe not the arc as a whole, but the subplot about saving Trixie, which runs through a good chunk of it.
Strife, Discord's sister, could arguably be said to be the Big Bad of the Generational Transition arc, as of all the Draconequi she was definitely The Heavy of the arc, and also served as the Final Boss for the last survivors of the Gen 3.5 universe. Though, she was just doing her job and was trying to give them a chance to prove their right to exist.
Bright Eyes' story has the Shadow of Existence of Discord's brother D___t, who briefly poses as her Enemy Within Cruel Eyes, and tries twice to absorb her soul and potential Concept in order to reconstitute himself. He also spends the entire Nightmares section stalking her as a presence she feels lurking over her whenever she feels emotionally vulnerable.
Clover's story, after a few wannabes, gets the closest thing to main antagonist in the shape of The Master — no, notthat one, who also exists in this universe. This one, who turns out to be a Diamond Dog named Fluffy the Terrible posing as an old unicorn, uses an army of ponies he conditioned as orphaned foals to run a slave-powered mining operation that Clover's family eventually stumbles on. And he proves how dangerous he is by killing Scout. That said, her Final Boss ends up being a group of Eldritch Abominations so dangerous that Fauna Luster and Entropy worked together to seal them away, and who try to trick Clover into freeing them.
One could also argue that even when Discord is the Big Bad, the series still has a Bigger Bad in his father Havoc — after all, he's the one who created Discord in the first place, and is also responsible for pretty much everything he's done in Equestria since he fed Discord his own brother (as well as Havoc's own avatar) in order to increase his power, before having him reborn in the mortal world. He was also the Disc One Final Boss of Origins.
Ace Combat The Equestrian War has Red Cyclone, a malicious griffon soldier who, alongside his comrade Black Star, overthrows the good ruler of the Griffin Kingdom and plunges Equestria into a time of war. His reason for doing it is to enslave or kill all ponies, as he believes they are weaklings that spoil his ideal vision of the world.
The Legends of Equestria continuity introduces The Emperor, the lizard-like leader of an ultra-advanced race that controls a planet-wide empire, of which Equestria is "but a speck". When Celestia and Luna first overthrow Discord, he shows up to assert his control. Being unable to defeat them in single combat, he vows to return with his army should they ever lose control of the kingdom.
In the Tamers Forever Series, BlackWargreymon fills this role in the second book Omni-Tamer by virtue of being the only recurring threat.
In the third book: Forget the Y2K, This is Madness!! the sadistic Nightmare virus becomes the prominent threat to the Tamers
However the Nightmare itself pales when compared to the overwhelming power of the psychotic Daemon, who sends his Agent to weaken the Tamers during the fourth book: Theory of Chaos, before terrorising them personally throughout Silent Sorrow
In Clash of the Elements this trope is Zig Zagged a few times. At first Cackletta looks to be the main villain, but then Joe Dark takes over after Alex defeats her. Then this looks to be switched AGAIN in a case of Hijacked by Ganon and Demonic Possession via the Dark King only for Joe Dark to regain control, but then it is revealed in the epilogue that Cackletta is not only alive, but is working with Dimentio and Smithy, setting up possibly a Big Bad Ensemble, but then as it is revealed in Part 2, Both of them were Cackletta's pawns, meaning that she is the true Big Bad of Parts 1 and 2 all along.
Alex has the titular antagonist herself from an Adventure Time fanfic. It turns out she's the Big Bad of the animated series all along, commanding the likes of Ice King, Ash, and Door Lord to do her bidding.
The Chaos Verse (an official spinoff of the Pony POV Series) has Nightmare Phobia. Interestingly, in addition to being the main antagonist of the story, she's also stated to be behind many events of canon by manipulating ponies (including the Mane Six) through their fears.
The Powers Of Harmony: After a lot of buildup, the mysterious entity Cetus reveals herself as the main antagonist. She turns out to be Nightmare Moon's Echo, and is planning to take over Equestria and then to complete Nightmare Moon's goal.
In With Strings Attached, there are two: Jeft, who was responsible for all the crap in the Second and Third Movements, and Brox, whose machinations are responsible for the Fourth Movement.
The Big Time Rush fanfic Big Time Obsession has Hyde, the serial rapist/killer who terrorizes BTR (mainly Logan) and their friends througout the story. Turns out he is really one of many multiple personalities of Detective Simmons. And even in that case, Hyde tries to manipulate the other voices to his will.
Yugioh The Thousand Year Door has the Shadow Queen, whom plots to defeat the heirs to the Three Heroes who defeated her so she can escape her palace, unable to leave it until she does so due to the curse the Three Heroes placed on her.
Gouki Namikaze in A Growing Affection is the ultimate Big Bad; he is Pein and Konan's second teacher and they are working for Madara on his orders, both to reign in Madara and to enable Gouki to take control of Madara's plan if it works out. In book 2 Madara was the Big Bad, before Gouki comes out of the shadows.
In Perfection Is Overrated, The Usurper directs the SUEs in their efforts to defeat the Himes. He even possesses the Obsidian Lord, the canon antagonist, but is killed after his minions are defeated and the Obsidian Lord is forced from Reito's body.
The Lunaverse's overall Big Bad is Corona, the struggle with whom forms the series' Myth Arc. However, as she's left severely weakened in Season 1 by her first confrontation with the Elements of Harmony, she ends up sharing the role with the cabal of corrupt Night Court nobles led by Duke Greengrass. But with their defeat in At The Grand Galloping Gala, Corona is free to take back sole Big Bad duties in Season 2 as she increasingly regains her powers.
The Conceptivore is the big bad in The World Of The Creatures. It's an idea-eating thought monster that invades peoples' minds and brings to life the total sum of all their thoughts/feelings/experiences/etc. just so that it can devour them, leaving the victim with no sense of self.