"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".
For the upcoming Mortasheen RPG, the genocidal, anti-monster, kill-all-mutants city of Wreathe counts as this in general. For a specific individual the computer A.R.E. best counts as this
There are plenty of people in Warhammer 40000 who could make claims for this spot:
Abbadon the Despoiler. Warmaster of Chaos. 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. 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.
The Tyranids. 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 kill every living thing in it, and the scary thing is that at the rate they're going, they will very likely succeed.
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 have go into straight up conflict with him.
Divis Mal from Aberrant is probably the biggest candidate for being a Big Bad, though there are definitely other threats out there.
The Warhammer Fantasy setting also has its share of these guys, notably Chaos warlord Archaon (Abaddon's fantasy counterpart), Malekith the Witch King, Grimgor Ironhide (Ghazghkull's fantasy counterpart), and the Skaven Council of Thirteen.
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.
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 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.
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 undead lord), 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.
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.