"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.
The RPG fandom likes to use the full Big Bad Evil Guy name or its initialism "BBEG".
Divis Mal from Aberrant is probably the biggest candidate for being a Big Bad, though there are definitely other threats out there.
In Blue Rose there is Jarek the Lich King, who isn't just the worst villain around, but actually one of the few truly evil characters in this very idealisticsetting. In a world where most antagonists are misguided, or weak-willed and fallen to temptation at worst, Jarek is just plain bad to the bone.
The Big Bad in Dungeons & Dragons varies between settings and editions, but the recurring cast is Asmodeus (a Satan stand-in), Vecna (the god of the liches), Tharizdun (the god of Omnicidal Maniacs), Orcus (a ridiculously powerful demon lord who rules the undead), and Lolth / Lloth (the goddess of the eeeviiilll Drow).
Tharizdun could be seen as the Bigger Bad, because as of 4th Edition he is responsible for the current evilness of all of the above villains except Vecna, and in Demonomicon it is explicitly stated that the shard of evil he created the Abyss with gave him a huge power boost. Since he was already a god this makes him the most powerful being in the setting, strong enough that the level cap of 30 isn't high enough for the characters to fight him.
In terms of overall campaigns, Vecna's one of the more common, and it's implied that his ascension to godhood was one of the key factors in the storyline changes between 2nd and 3rd editions.
Eberron has a wide variety of potential Big Bads, fittingly for a DnD setting designed to provide challenges for a wide variety of stories and player power levels:
The Biggest and Baddest are the Overlords, who straddle the line between Demon Lords And Arch Devils and God of Evil and ruled the world millennia ago, but are currently all Sealed Evil in a Can, and are therefore forced to work through their less powerful (but still incredibly nasty) minions, the Lords of Dust. They're far from the only nasties out there, however.
The Kalashtar vs. Inspired subset of the Myth Arc has the Dreaming Dark, which seeks to control all mortal dreams and already rules The Empire of Riedra through the Path of Inspirationnote Word of God from setting creator Keith Baker puts the Dreaming Dark collectively at roughly the same level of power as a single Overlord.
Then there are the Daelkyr, Humanoid Abomination rulers (maybe) of the plane of Xoriat, who view destroying worlds as a form of art and tried to destroy Eberron millennia ago; while they were stopped, several Daelkyr remain imprisoned on the mortal plane and, like the Overlords, they have their share of minions of worshippers still active.
Erandis Vol, the Lich Queen, can't really compare to any of the above in terms of raw power, but she's had several millennia to spin plans and has her fingers in lots of pots across Khorvaire, and she also helped create one of the setting's major religions.
On a more mundane level, the Aurum are a conspiracy of wealthy and powerful merchants and aristocrats who seek to control Khorvaire from the shadows.
Perhaps the least powerful, but most iconic (to the point that he made it onto the cover of the Fourth Edition setting book), Big Bad of the setting is the Lord of Blades, a renegade warforged who seeks to subjugate living beings to his kind (and possibly become a god in the process). He was designed as an antagonist in the vein of traditional supervillains and is frequently compared among fans to Doctor Doom and/or Magneto.
Though those are the main "unambiguously evil" threats facing Eberron, the setting's use of moral ambiguity and Grey and Grey Morality means that even some of the more seemingly benevolent or neutral organizations (the Dragons of Argonessen, the Undying Court, or the Dragonmarked Houses, for example) can be potential Big Bads if the PCs get mixed up the wrong way in what they're doing.
In the Greyhawk campaign setting, the evil demigod Iuz the Old is probably the most prominent because he actually lives on Oerth (although so do some other evil demigods). There are also a wide variety of others.
In the Ravenloft setting, the Darklord of each of the Domains is this. Neatly organized too, since they are both the rulers and prisoners of their Domains.
Exalted has the Deathlords, ghosts of powerful First Age Solars — pinnacles of super-human achievements — who now serve the Neverborn. Arguably, the biggest and baddest of them all is the First and Forsaken Lion.
The Ebon Dragon embodies the principle of Big Bad-hood and is running the plan to reclaim the world with the Scarlet Empress as his thrall. And he was one of the creators of the world. In fact, he created the God ofHeroism solely for the purpose to define his own existence.
Chejop Kejak can be seen as the Big Bad for the returned Solars. The Sidereal old man engineered the Usurpation of the Solar Deliberative! ... Well, he had his reasons.
Dr. Methusala. This guy is so much more powerful than any other character that the book suggests you treat him as an event, rather than go into straight up conflict with him.
Tech Infantry has a variety of Big Bads, from The Bugs, to Rashid King, to Modred. Ultimately, the biggest bad of all is the Crapsack World nature of the universe itself.
The Warhammer setting has its share of these guys, notably Chaos warlord Archaon, Malekith the Witch King, Grimgor Ironhide, and the Skaven Council of Thirteen.
There are plenty of people in Warhammer 40,000 who could make claims for this spot:
Abbadon the Despoiler, Warmaster of Chaos (Archaon's sci-fi counterpart). Has led thirteen Black Crusades against the Imperium from the Eye of Terror. Thankfully, they were all stopped from reaching Terra, although each time, millions of innocent people on dozens of worlds died.
Ghazghkull Mag Uruk Thraka (Grimgor's SF counterpart). An Ork Warboss the size of a Dreadnought, making him the biggest and baddest Ork in existence. Claims to receive visions from the Ork gods telling him to unite all the Orks in the galaxy under a big WAAAAGH, and already has millions of Orks under his banner.
The C'Tan Star-Gods. One of them, the Nightbringer, is responsible for making every living thing fear death.
Asdrubael Vect, the de facto kingpin of the Dark Eldar. Every Dark Eldar raid and attack in the galaxy from the last few thousand years can be traced back to this monster. Oh, and the Dark Eldar's ancestors were responsible for creating the Chaos God Slaanesh, and the previously mentioned Eye of Terror.
The Tyranid Hivemind. As a faction, they're a good contender for the overall Big Bad of Warhammer 40000. Consumed thousands of worlds, and it is hinted that everything we've seen so far is just a tiny percentage of what they're capable of. Their goal is to sweep through the galaxy and eat every living thing in it, and the scary thing is that at the rate they're going, they will very likely succeed.