Tanar'ri
These are demons, the chaotic evil supernatural badguys, in 2nd Edition Dungeons and Dragons. After TSR got their new CEO Lorraine Williams and Gary Gygax left in disgust, the company decided that nutcases like Jack Chick and Patricia Pulling had to be pandered to, so Williams said "no more demons, or any of that junk". In 3e they wisely decided to use "demon" again, but kept the term "tanar'ri" as a subtype of demon. Since TSR bothered to register "tanar'ri" as a trademark, you will not find this demon subtype in Open Gaming License materials like the D20SRD.
They are the archetypical chaotic evil outsiders, seeking to destroy all order and plunge creation into mad, violent chaos in different ways. They are one of the two major factions in the ideological Blood War, the other being their lawful evil counterparts, the baatezu, or devils.
Fiendish Codex II - Tyrants Of The Nine Hells states that Devils call all demons Tanar'ri for short, which is strange considering that in the same book it says that in the language of the devils "only one correct way exists to construct any given statement in Infernal." It also states that devils "except when in disguise, they find the urge to correct errors in spoken or written Infernal nearly impossible to resist." This may be a hint as to the origin of Lorraine Williams, since she also insisted on using the term "tanar'ri" instead of "demon."
Demon Lords
The first amongst the demons, the lords of the Tanar'ri (more commonly known as Demon Lords) are some of the most powerful, dangerous, cunning and deadly beings in existence. They attained their position by strength of arms and cleverness (mostly the former) to rule over their servants. Those who wish to challenge their lords are quickly struck down as an example and to keep the other minions in line.
Baphomet
Baphomet, the lord of the minotaurs, is a massive bull-headed brute. He revels in combat, but prefers to put his powerful-looking opponents into a magical maze and trample the smaller ones before crushing the big ones. His most common followers include minotaurs, bulezau and goristro demons, fiendish or half-fiendish minotaurs and Awakened animals such as dire animals or dinosaurs. His ultimate goal is nothing less than the destruction of all civilization, and the descent of all life into violent, bestial savagery.
Baphomet's cult is on the rise, often finding worship in rural areas by evil druids and rangers, preaching the gospel of a nature deity of vengeance that will deliver the common folk from the evil machinations of city-dwellers, eventually swaying them to his cause. From there, armies of fanatical Luddites, many bearing physical manifestations of his influence, swarm out to raze towns and slaughter those who live in them.
Baphomet lives in the Endless Maze, the 600th layer of the Abyss. He shares this layer with the Obyrith Pale Night, with whom he has some kind of understanding: neither of them encroach on each other's territories and they will help each other when one of them is invaded by one of their foes.
Demogorgon
The current Prince of Demons, a title largely contested only by Orcus and, to a much lesser extent, Graz'zt. He has the shape of a two-headed baboon with tentacles instead of arms. His left head is called Aameul and has a silver tongue that can charm any creature, while the right head, Hethradiah, can cause insanity. They seek to dominate or kill one another, just as their combined self seeks to slay or overpower all life. Demogorgon is a fearsome foe in battle, capable of rotting flesh from bones with but a caress of its tentacles and can drain the energy of anyone slapped by its tail.
Demogorgon has few followers amongst the humanoid races, but he has many amongst the more monstrous people. Yuan-ti, troglodytes, ixitxachitl and hosts of demons worship Demogorgon as their lord. These cults are depraved and engage in all manner of horrific rituals and sacrifices to their lord. Humanoids rarely worship him as cults, but individuals dedicated to the Prince of Demons tend to be just as dangerous, given that they are quite often high-ranking members of society, and his influence is thought to be the source of many monstrous versions of natural creatures, like ettins and merrow.
Demogorgon's layer of The Gaping Maw is the 88th of the Abyss. While it's a tropical realm with plenty of water it is not a hospitable plane, with many different kinds of demons roving the surface and the ocean looking for things to devour. Demogorgon runs the great city of Lemoriax that is one of the premier slave markets in the Great Wheel. He frequently stalks through his city to whip his followers into a frenzy. His layer is linked to the next layer, Dagon's home of Shadowsea. The two are allied, which effectively means they stay off of each other's backs.
He was also a motherfucker of a bonus boss in Throne of Bhaal, even if actually fighting him was definitely not the smart move there.
Fraz-Urb'luu
The Prince of Deception, Fraz-Urb'luu is a great pale plue winged monster with surprising magical ability. He is the patron of evil illusionists and tricksters, so powerful that he can easily summon demons and even other demon lords, though he prefers to not do the latter all that much because does not want to piss Demogorgon off any more than he already does.
Fraz-Urb'luu was one of Zagig's prisoners below Castle Greyhawk, trapped in a bas-relief for more than two centuries. When he was finally freed by a bunch of adventurers, whom he repaid by wrecking their gear and casting them into the Abyss. What a dick. Back in the 176th layer of the Abyss, Hollow's Heart, he spent time rebuilding his realm and searching for his magic staff. If he succeeds, his first order of business would be to visit terrible vengeance upon the world of man.
Cults of Deception pose as cults of exiting but obscure deities and try to convert people to their cause... only to be sacrificed to the Prince of Deception. His followers include large numbers of other deceptive dmons, including succubi, lilitu and a group of Chaotic Evil Rakshasa called the Hollow Rajas.
Graz'zt
The Dark Prince Graz'zt is something of an anomaly amongst the princes of the Abyss. While the others all possess some degree of cleverness, at the end of the day they will use brute force to get what they want. Not so much in Graz'zt's case. He is skilled in the ways of seduction, guile, politics and plotting in ways that go beyond the abilities of even the most intelligent princes of hell. 4e suggested that this is because Graz'zt is an exiled devil, but this is the only version that posed this option. While by far the weakest of the three in terms of raw hitting power, Graz'zt's genius and cunning ensure that he remains a strong rival to both Demogorgon and Orcus.
He resembles a tall, handsome humanoid with goat legs, horns, six fingered hands and yellow eyes that betray him for what he really is. Graz'zt has a massive libido and counts many female priests, succubi, harpies, mariliths, lamia, you name it amongst his followers, with the odd male equivalent here and there for variety's sake. The closest of these are called the Chosen (with the suggestion he chooses them to join him in his bed). He also has more offspring than any other demon lord, with many of the closest members of his court, including his chief general and personal assassin, being his own children.
While he is of great intelligence, he has met his match in a mortal, the witch-queen Iggwilv. She managed to trap him on the Material Plane to learn from the demon. The two of them eventually became lovers, culminating in the birth of a child. Said child turned out to be Iuz, who became a major player in the world of Greyhawk. Graz'zt slowly figured out that Iggwilv did not want to let him go back to his home. So he waited and plotted, eventually breaking free in a battle that cost Iggwilv most of her resources. But she escaped and was lured into the Abyss by the Dark Prince. She in turn was used by Graz'zt to regain his lost powers and grow stronger before she escaped. The two of them are currently in a mutual love-hate relationship, each trying to exploit the other to increase their power even as, to the extent that either of them are capable of positive emotions, they genuinely enjoy one another's company.
Graz'zt's realm is the largest in all of the Abyss. Covering the 45th, 46th and 47th layers of the Abyss, Azzagrat's primary attraction if the city of Zelatar, which somehow exists on all three layers at the same time. Each layer hosts a different neighbourhood, and Graz'zt's citadel on the center layer. It is also one of the more popular destinations in the Abyss for travelers to visit, featuring markets full of rare goods and comparatively better-behaved demons, but those who think that that translates to "safe" are as foolish as those who think that Graz'zt's hedonism and hunger for pleasure over raw power makes him any less evil or dangerous than the likes of Orcus or Demogorgon.
Jubilex
The Faceless Lord Jubilex lords over all oozes, slimes and jellies. This is not a paricularly difficult task given the mindless nature of these creatures and Jubilex' lack of tact regarding such issues. He resmbles a massive puddle of green slime filled with eyes swimming around in it and pseudopods drippingwith ooze. His goals are simple: destroy everything that is not like him. He wants to kill and corrode everything in existence, destroying whatever it can touch with its oozing appendages, until all life, everywhere, is as formless and protean as he is. This makes him very unpopular with the other demon lords and all stay away from his layer as much as possible.
Jubilex has few cultists given that his charges are almost exclusively of low intelligence. When a deranged humanoid takes up the worship of the Faceless Lord it is quite possible that Jubilex doesn't really care about these worshippers, and even when an intelligent ooze such as Darkness Given Hunger, a Black Pudding possessed by a Hezrou, worships him, Jubilex cares little.
Jubilex lives on the 222nd layer of the Abyss named Shedaklah. He contests for control of this plane with Zuggtmoy, the Queen of Fungi. While she had the upper hand for a while, since the events with Iuz and the famous adventure in the Temple of Elemental Evil, Jubilex has gained a lot of territory, currently battling with the forces of the Queen of Fungi and slowly gaining ground.
Lolth
The Spider Queen is a former elven goddess, and is now the ruler of all drow, spiders, poison, and other fluffy things. So popular she has her own page.
Malcanthet
Malcanthet, the Queen of the Succubi is a being of unparalleled beauty and cruelty. Taking the shape of an alluring succubus she prefers to let others do the fighting for her, either summoned minions or enslaved attackers. Befitting her status of the Queen of the Succubi she really gets around: aside from her usual trysts, she has Pazuzu and Demogorgon as her most frequent lovers, having sired several powerful succubi with the former and and unspeakable abominations with the latter. She has had short affairs with most of the other demon lords at some point or another, but these were mainly flings for her private benefit. Yeenoghu is one of her enemies, the two of them still being embittered by the other foiling their plot to corrupt the same family of nobles, ending with the entire family being destroyed instead. Her relationship with Graz'zt is even worse: each claims that the other spurned their advances, and, deeply embittered, the two have been at war ever since. Her servants include, aside from succubi and lilitus, lamias, harpies, and fiendish nymphs.
Malcanthet lives on the 570th layer of the Abyss, a layer called Shendilavri. It is of unmatched beauty, surpassing even some of the heavens as a paradise. Here she lives in the city of Rivenheart, where all desires can be sated. Every imaginable perversion, debauchery and experience can be found here. Malcanthet's palace has no doors, and all are invited to enter and experience what lies within its forbidden halls. While thousands of people from all over the planes enter to find bliss within, few leave, and all ultimately realize that Shendilavri is a paradise only for Malcanthet herself.
Miska the Wolf-Spider
The right-hand man and lover of the Queen of Chaos, Miska the Wolf-Spider is one of the most dreaded demon lords in existence. Resembling a nightmarish Drider with a spiked and armored spider lower body, the upper body of a pale, handsome, four-armed human with long black hair and a pair of red-haired wolf heads sprouting from his shoulders. Once the foremost servant and lover of the Queen of Chaos, she appointed this Tanar'ri as the Prince of Demons, the first to bear that title. This, combined with Miska's skill as a general and a warrior and the victories he achieved massive numbers of demons flocked to his service. Eventually he was defeated at the Battle of Pesh, where one of the Wind Dukes of Aaqa pierced him with the Rod of Seven Parts. The Prince of Demons wailed in anguish as his blood covered the Rod, corrupted and shattered it. If it had not been for the Rod breaking Miska would have perished, and instead he went through a planar rift. Some of th Wind Dukes followed him, imprisoned Miska and the citadel he was in in a great cocoon of pure law and cast him into the depths of Pandemonium, where he remains to this day.
In his prison Miska can do little harm, but only partially because of the prison itself. When he was injured by the Rod of Seven Parts his abilities were crippled, rendering him at only a shadow of his former self. On the other hand this made him next to indestructible: even if he were to be turned to ash he can simply rebuild himself. If he were to get his hands onto the fully restored Rod of Seven Parts he would be fully restored and become able to leave the cocoon of law to join his beloved Queen and continue on their bloody crusade. The plus side to this is that restoring Miska to his full powers will make him vulnerable again, and allows for him to be permanently destroyed.
Actually destroying him is a daunting task: his armored body is resistant to blunt weapons, and slashing and piercing weapons draw his acidic blood that is both dangerous to an attacker and their weapon. It is in fact so lethal that it might kill an attacking instantly and disintegrate a weapon coated in the Wolf-Spider's blood. Miska himself wields deadly weapons in is powerful arms: a scimitar that can disintegrate lawful opponents, one that strikes at blinding speeds and two magical morning stars, each of whom he wields with deadly precision.
Miska commands the respect or fear of the Spyder-Fiends, monstrous spiders with the heads of wolves and clawed humanoid arms in the more powerful cases. While some resent serving Miska, they do not dare anger him or his master, the Queen of Chaos.
Orcus
Looking and acting like the forbidden lovechild of Khorne and Nagash, Orcus is the Prince of the Undead. He has his own page, which can be found here.
Yeenoghu
The King of the Gnolls, Yeenoghu is a savage beast. Despite not being the most powerful of the demon lords, his savagery and that of his followers still makes him a powerful opponent. This became clear when he and his forces invaded the layer above his own, the White Kingdom. This layer was ruled by Doresain, the King of the Ghouls. When his armies were destroyed, Doresain swore fealty to Yeenoghu for the sake of self-preservation, forsaking his old master Orcus. Because of Orcus' recent plots his attention has been elsewhere, and it is as of yet unknown how he will reply to this treason.
Yeenoghu's greatest desire is to have the Material Plane inhabited by his chosen people, the gnolls. A world where his people are the dominant race, and all humans, elves, dwarves and halflings are either slaves or food. But he understands that gnolls alone are not numerous enough to achieve this goal, and as such he allows cults of other races to serve him. One of the most powerful of these cults, originating from the Maure family, was finally getting somewhere when Malcanthet also tried to corrupt them, resulting in a self-destructive downward spiral that wiped out all of the humans. They have resented each other ever since, with Yeenoghu sending frequent raids into Shendilavri to destroy it. These attacks have always been held at bay, but he hopes to one day destroy her and her realm. The King of the Gnolls also has a violent hatred for Baphomet, perhaps due to their similarity, against whom he frequently wages war to little result.
Yeenoghu's realm is called exactly that, Yeenoghu's Realm, perhaps reflecting its master's lack of imagination. Located on the 422th layer of the Abyss it is covered in a great savanna where packs of feral gnolls, other hyena-like creatures, and worse monsters make their home, preying on visitors, one another, and even the servants of Yeenoghu. The King of the Gnolls himself lives in a great palace drawn by thousands of slaves across the plane past various points of interest at a speed of about one year per round.
Zuggtmoy
Zuggtmoy, The Queen of Fungi is an ambitious but not very successful demon lord. Given her domain over fungi and mushrooms she has difficulty finding people to worship them. So she opts with having to disguise her influence, creating cover cults that her own followers kept in line so that they could stay in charge. The Temple of Elemental Evil was such an endeavor, and it worked pretty well for a while, only for everything to spectacularly backfire when the Circle of Eight destroyed the cult and imprisoned her. She managed to escape the Material Plane at the cost of a good deal of her essence, only to discover that her enemy Jubilex had conquered a good deal of her home layer in the meanwhile.
Aside from her rivalry with Jubilex, she has frequently been at odds with Lolth prior to her gaining significant power as a deity, putting her a class above the Queen of Fungi. On her home layer of Shedaklah she lives in a palace built from the largest fungi in the multiverse, rising more than four miles into the air. Here she conducts horrific experiments and plots to gain foothold on the Material Plane and to defeat the hated Jubilex.