Primordial
Primordials in Exalted are the original gods of creation, birthed from chaos and responsible for just about everything that came after them. They are inscrutable to the point of being Lovecraftian, and tend to focus on one concept to the exclusion of all else. To simplify it primordials are the ultimate munchkins. They're beings so hyper specialized that not only can they not perform tasks outside of their purview, they can't even understand them on a conceptual level.
Although they were originally all bros the primordial war split them into two groups. The collaborators (who got cake) and the loyalists (who got soul lobotomies).
If looking for the elemental creatures Dungeons & Dragons 4e called by this name, check out the Archomental article.
Intact Primordials
Originally all the primordials were alive, but following the great war only two remain.
Gaia: Mother of creation. Being one of the few primordials with anything passing for empathy she wisely sat out the war and survived. Wandered off the edge of nowhere looking for answers and hasn't come back since.
Autochthon: The great maker. Got sick of his jerkass brothers and sisters wrecking his crap and sided with the humans (after operating on his fetich soul to install learning). Like the flatmate of a sociopath he got a little worried about sharing creation with the now triumphant (and cursed) exalted and decided to sleep outside. Currently has a terminal illness that runs around his body trying to murder the people living inside him, who already had enough to deal with from the fact that his genius never led him to invent the safety rail since machines can't hurt him.
Yozis
Malfeas, the Demon City: The Maniac-Depressive former king of the Primordials. Even when he was intact he had problems wrapping his head around the concepts that other beings had opinions, or that he should care. Currently sewed inside his own stomach imprisoning his kin (or, if you're feeling unkind, turned inside-out and shoved up his own ass), he wants nothing more than to flip the proverbial board on Creation and start over, though only after torturing everything in it to death forever. Hates everything and everyone in Creation... but hates himself most of all.
Cecelyne, the Endless Desert: One-time head judge of the primordials and current insane desert, Cecelyne surrounds the Realm of Malfeas in an endless expanse. Her laws aren't as popular these days and mostly consist of "if you can kill it, then it belongs to you," as part of a big, nihilistic thingummy to show the meaninglessness of all law. Word of God says that she is Borderline Personality Disorder incarnate.
She Who Lives In Her Name, the Principle of Hierarchy: - Obsessive-Compulsive She Who Lives was in charge of order and hierarchy back in the day, and recent events have only reinforced her longstanding belief that freedom is the problem with creation. She was only narrowly convinced to give her exalts free will, and seeks to rectify the condition whenever and wherever she can.
Adorjan, the Silent Wind: Once Adrian, the river encompassing creation, she had her Fetich soul Lilike killed in the primordial war and turned into a howling windstorm. She's not really mad about it though. In fact she's happy as can be. She loves creation, she loves exalts, and she'd love nothing more than to summon up her winds and give you a big hug. Her exalts get a charm to instantly fall in love with people and then get bonuses for hurting them.
The Ebon Dragon, the Shadow of All Things: The original sociopath. The elemental embodiment of dickishness, or more simply, opposing other beings from their goals, which is about all he knows how to do. He is the least mutilated of the yozis due to a timely surrender and is still capable of (mostly) rational thought. As such he is one of the prime movers in the demon city. He was responsible for cursing the solars (well telling the others how to do it and fueling it with their dying breaths) and was the driving force behind the Green Sun Princes. He is basically backstabbing everybody all the time, and if Return of the Scarlet Empress is to be believed he is so irredeemably treacherous even his own component souls are scheming against one another. Oh and he's also a stalker
Kimbery, the Sea That Marched Against the Flame: The suffocating control freak to Adorjan's deranged stalker. If you're on her bad side she'll consume you under her acidic waves. If you're on her good side she'll lavish you with affection (usually in the form of acidic waves). Nobody survives Kimbery's attentions for too long one way or another.
Cytherea, the Mother of Creation: The Divine Ignition, she is the Big Bang itself. She helped wake the primordials and build creation. Beyond that not much is known about her.
Oramus, the Dragon Beyond the World: The eldest primordial and arbiter of creation. The solars were so afraid of him and his ability to escape any boundary that they locked him in the only prison he could never escape: his own wings. So now the universe's most powerful reality hacker is trapped inside himself more and more insane. Needless to say, shit is going to get fun if he ever escapes.
Isidoros, the Black Boar that Twists the Skies: A yozi who takes the form of an unstoppable rampaging black hole in the shape of a boar. Likes screwing destiny and penetrating things, dislikes rules and inevitability. Unsurprisingly the cause of mountains of slash fic both in and outside of canon. Currently in a bromance with Szoreny that may or may not include a "b".
Sacheverel, Who Knows the Shape of Things to Come: The Abhorrent Prophet Unimagined. Another yozi who had his fetich soul killed (because that's always a good idea) and turned into a deranged seer as a result. While he sleeps he sees infallible visions of the present. If he should ever wake up he will see infallible visions of the future. Nobody wants Sacheverel to wake up.
Hegra, the Typhoon of Nightmares: A storm of emotions and patron of traders. Spends most of her time terrifying people's dreams.
Elloge, the Sphere of Speech: Another victim of Fetich death, Elloge got gender swapped and turned into a silently moving sphere of linguistic concepts. Unlike most Fetich deaths, not overwhelmingly terrible for everyone as a result. If you stumble into her by mistake prepare to engage in narrative kung fu battles with the past participle tense.
Szoreny, the Silver Forest: A giant silver forest and mimic. Szoreny loves you, Szoreny hates you. He's the quickest way to travel around Malfeas if you don't mind running through a twisted house of mirror inhabited by clones. Probably the least maniacal of the Yozis, he's working on getting a pardon for himself and his sometimes boyfriend Isidoros so he can have his revenge at long last live in harmony with creation. (Which may or may not involve conquering it first, but go back and read Malfeas's entry if you don't think that still qualifies him as "least maniacal.")
Metagaos, the All Hunger Blossom: OMNOMNOM.
Neverborn
Some of the Primordials were slain before they could surrender, struck down by the likes of Ghost-Eating Technique and other such spirit-destroying powers. Since primordials can't even conceive of death, let alone think to program the reality they built to handle their deaths, reality promptly shit a brick and jammed. Now they sit trapped between existence and nothingness, whispering to people about how they should really consider the merits of killing everything everywhere forever.
Abhorrence of Life
Father of Murder
He Who Holds In Thrall (while none of the Neverborn are really unique characters, this one was probably Mardukth)
Perfected Principle of Consumption
Tears of Want
Whose Whispers Chain
The Dragon That Was - What the fuck did you do? If this guy shows up in your campaign it means you killed the Ebon Dragon (somehow?). There's not much fluff on what this means, except that its guaranteed to be bad.
The Engine of Extinction - Similarly this is the result of what happens if you killed Autochthon, or let him die or whatever. Congratulations on turning one of the few benevolent cosmic entities in the game into the rape-o-matic 9000.