Of the three Hellish Planes, the first one to exist was Thanatos (word meaning destruction), and this is the plane where demons live in. These are, in addition to evil, of a generally chaotic alignment, something that can be seen as they generally have a monstrous appearance. Usually, they are the strongest physically, and the most bloodthirsty and impulsive. Therefore, we cannot say that the Demon Princes are genuine rulers, because Thanatos is too chaotic for the existence of something like a minimally stable and controlled society. They are simply the most powerful and strongest amongst them, and the rest of demons obey them for sheer terror at the prospect of unbridled anger. And among them there is no other hierarchy than that of the more powerful over the weaker (although talking of weakness in any case is an euphemism). From a mythological or theological view, the Demon Princes are also embodiments of monstrosities of all kinds, and idols of savage and primitive mortals. The following list is not exhaustive, so inventive gamemasters are free to create new Demon Princes at their convenience; but hopefully you will find here everything needed to develop an adventure or campaign.
Ahrimanes is a Demon Prince particularly ugly and hideous: it has three feints of faces in his head, "feints" because they have only two atrophied vestigial eyes and holes filled with crooked teeth in the manner of mouth, from which perennially arises an incredibly breath foul; the head is surmounted by three curved horns. His repulsive appearance is enhanced by being always surrounded by an almost solid darkness, moving with him. According to some legends, this horrible demon was the first fiendish creature to put its feet on the material plane; habit that still keeps today, and it's from him that emanate many of the terrestrial monstrosities. Anyway, despite what might be thought, he's not a too powerful demon; although his importance lies, not only on his horrific appearance, but on the fact that he's one of the oldest inhabitants of Thanatos, one of the first born; and that's enough to earn him the admiration of other younger demons.
This Demon Prince looks like a giant horse, equipped with exceptionally strong muscles and a fur as black as the darkest pits of hell, fur that is marked with many scars that give off a bloody and sticky ichor. His eyes shine like two red-hot irons, and it's hard not to die of terror in front of his eyes full of anger; and if that fails, his breath is fatal. He lives buried in the depths of Thanatos, and it's almost impossible to find on the surface; it is assumed that he also likes to move around the earth elemental plane. In Ajsalium he's especially feared by dwarven miners, and there are numerous accounts from survivors of catastrophic collapses in mines which claim that they were caused by Aneberg, and that the unhealthy gases in mines are but his breath.
This female demon is, in many respects, an exception to the rule that dominates the looks and habitual tendencies of the rest of her species. In fact, Astartea meets the schemes of the devils, and certainly would have moved to Avernus if not for staying with her husband Astaroth (see below). The case is that Astartea is very beautiful and elegant; she's got a pale complexion and rugged but beautiful features, she dresses with nice silks of the most elaborate softness, and adorned with threads of gold, silver, platinum, and other even more exotic metals. Her head is scalloped by the horns of a silver crescent moon, and in fact she's often taken as the "Lady of the Moon"; so she could be a renegade member of the race of angels who live there, or perhaps a descendant of the Rat who lived there for some time. His admirers often undertake, with each moon's last quarter, venereal rites full of sensuality.
Astartea's husband, Astaroth seems almost her opposite; it's hard to imagine a couple with most different and opposed appearances, and impossible to guess the motives of their union. For everything that Astartea has of beauty, Astaroth has of repulsiveness: perhaps only Ahriman is as ugly and nauseating. Astaroth is a grotesquely fat demon with nasty habits, dropping saliva off the corner of his lips and mucus from the nostrils. Also, the stench is for him a business card which precedes him whereever he goes. And despite all that he enjoys some popularity among mortals, because in Thanatos he's the Prince in charge of custody of the hoards and treasures, which they like to accumulate despite their futility at the hellish planes. Another of his attributes is being patron of insects, especially of the most annoying ones, and it is said that he leverages the height of summer to launch his army of hornets, mosquitoes and the like all over the world, to inflict small torments to mortals.
One of the most famous Demon Princes, it's also common referring to him in books as "the messenger", because his role in the demonic host is being the prime standard bearer of the demonic armies. That makes him the right arm of Baal, and one of the greatest allies of Beelzebuth. Azazel's appearance has become a typical image to represent the fiendish creatures: it is a male goat that walks upright like a humanoid. His physical strength is very considerable, and his determination on the battlefield absolutely unwavering; the banner that he bears, in addition to its terrifying magical powers, is topped with a sharp blade with which he cuts the throat of anyone who puts in front. The rituals in his name include the sacrifice of goats to purge the sins that he would punish, whence comes the term "scapegoat."
Baal is probably the second most powerful Demon Prince, only behind Beelzebuth himself. He is the commander in chief of the demonic army, which he rules with absolute and uncontested authority, in addition to great intelligence and wisdom. His physical strength is immeasurable, and is his extensive martial skills, which he's always willing to put to practice, against both voluntary and forced opponents. Curiously, despite all these traits normally regarded as masculine, Baal is hermaphroditic, although his general appearance looks more masculine than feminine. His self-begotten offspring are some terrible winds that, from time to time, travel and plague Thanatos itself, and that reach the material plane, where during the autumn make leaves fall from the trees and extend the kind of death of nature which later remains during the winter.
Another major Demon Prince, especially for the minotaurs, for whom he's their patron, and presumably their creator. That should not suggest that his appearance is that of a minotaur, but he's a two-headed demon with the face of a beautiful woman on one side and a bearded man on the other, and yes, large bull horns. He supposedly created the minotaurs when he cursed a vain hero of ancient times who wanted to be as strong as a bull; the irrepressible sexual appetite of the created monstrosity caused it to become a race. Baphomet lives in a colossal labyrinth, the most difficult of all that may exist, because, in addition to its immense size and complexity, it constantly changes its layout. Only Eurynome (a Lord of Temptation from Inferno) got in and out of it, which humbled Baphomet so much and filled him with such rage that he tore Eurynome's eyes as punishment (such events are common among all the fiends).
This is one of the less powerful Demon Princes, but that does not prevent him from also being one of the most dangerous ones, even to their own kind. Behemoth is extremely clumsy and stupid, and many demons mock him right in his face; and although he's easily irritated, his clumsiness and slowness of movement does only take dodging to avoid him. His danger comes from being the Prince of Gluttony; his shape is that of a gargantuan ox (so big that it is incredible to believe even seeing with your own eyes). And this huge ox cannot stop eating for a moment, and can literally eat anything. So much so that they keep him chained and locked up almost all the time, because otherwise he would be able to eventually eat the whole plane of Thanatos. In fact, there is a terrible hole that stretches for hundreds of miles and is the result of Behemoth's constant devouring; and wise men don't forget the threat that hangs over mortals if he were released in the material plane.
Belzebuth is the undisputed leader of the Demon Princes. He's the most powerful of them all, and his power is only comparable, now, with that of Lucipher, with whom he devised the plan to get rid of Satan when his ascension to godhood broke the "feudal" balance between master demons and devils. He looks downright impressive, and has nothing to envy anyone: his size is prodigious, his forehead is encircled by a crown of fire, which glows as much as his menacing eyes. Other characteristic features are his huge bat wings and the horns, and the ability to breathe flames like a dragon; his general appearance is also a fiendish archetype. His name means "Lord of the Flies", as he is always accompanied by these nasty bugs (which makes him easily recognizable to any careful observer), and in fact he may take the form of a giant fly at will.
This Demon Prince is one of the most hateful and frightening. Among other titles, he's the proud holder of "Destroyer of Cities", which gives a clear idea of his concept on the fate of the life and works of mortals. This Prince of Annihilation only finds joy in spreading ruin everywhere, and his hatred of all that remains standing is inextinguishable. Fortunately, his power is not comparable to that of the major leaders; granted that that is little consolation to those who suffer his wrath, since the devastation caused by him always takes years to rebuild and regenerate. This extends to Thanatos too, where every building eventually undergoes his harassment, sooner or later; and in this sense Halfas is a good example of an extreme case of chaotic evil alignment, unable to make any distinction. Although preferably he likes roaming planes and places inhabited by beings of law, to destroy their buildings, which are usually neat and impressive.
As Astartea, Lilith is a happy exception to the common monstrous aspect of demons. This ancient Demon Princess is the Queen of the Succubi, the mother of them all, and the most notable for its irresistible charms. This "man-eater" (in the most sexual sense of the expression), within her evil still keeps tremendously attractive manners and attitude, so few are able to resist her advances. She feels a special fondness for human males, and it's said that when the first men appeared Lilith embodied in Ajsalium, copulating with them and generating the first half-demons, whose blood was then diluted in the entire human race (a theory supported mainly by elves and dwarves, but much less by human scholars). Anyway, Lilith's sexual appetite seems to be incapable of being ever satisfied, or at least there has been no consort of any race or species capable of leaving her completely satisfied; she is still searching.
Malthus is one of the Demon Princes most feared by all mortals, because its main attribute is being the Prince of Diseases. This also directly confronts him with the goddess Fiolsvinn (who is, among other things, a goddess of protection of life and health); a type of confrontation that most fiends don't follow because defeat is likely. What doesn't mean that almost every of them won't support the unwholesome activities of this demon; except those with a greater martial spirit, for whom it is a shame that an opponent die all by himself instead of killing him with their own hands. But Malthus, like a big kid, enjoys creating new diseases and indiscriminately disseminating them everywhere, including the material plane, where he uses rats and other strange followers to desolate the lands.
Mictlan is a Prince of Gluttony, like Behemoth, yet the differences are striking: while Behemoth is a clumsy and dumb ox whose eating habits are due to an insatiable hunger, Mictlan is governed by the true vice of gluttony, eating just for the sheer pleasure of eating, to the point of madness. This also extends to greed, to the excessive desire to accumulate and accumulate. The appearance of the demon does justice to his repulsive personality and sour character: his skin is dark and has a greasy luster, and from all body parts many tentacles sprout, with which he holds any edible object (if still alive, the better; and if they scream, much better). In his face stand his little and completely black eyes, small windows to his rotten soul, and, of course, a huge mouth in constant motion, always brooding with great pleasure and unpleasant pasty noises.
Moloch is well known to mortals, as he's one of the Demon Princes that hold more predicament among them in ancient times, and whose rites were more gruesome. His name means (or so the sages understand) "Prince of the Land of Tears", which has been linked to the extreme pain caused by the sacrifices that this demon has always required: babies and innocent children, who were to be teared apart, alive, and whose blood was for the cultists to bath in. In exchange for these bloody sacrifices Moloch offered fertility, both to humans and for agriculture and livestock. The idols carved in his image and likeness, always cast in bronze to reflect the blood of this demon, that is molten bronze, always carry a royal crown, and the head of some kind of beef (bull, ox, cow, or even buffalo), perhaps because of his popularity among the first farmers and ranchers.
Among the Demon Princes, Xafan is the youngest of them all, and the only one who actually has a sense of humor, albeit in the manner of a demon. He is totally immune to fire, and besides there is nothing he likes better in all existence. He spend as much time, or more, diving through they plasma of the elemental plane of fire as in Thanatos itself, where he always ignites huge bonfires in which to rest. The immunity does not prevent his body to get blistered and sore, nor his skin to be a bright red. His passion for the unbridled fire once led him to try to burn an entire heavenly plane; and although he didn't achieve his purpose, the temerity of such an act won him the sympathy of many fiends, and the other Demon Princes allowed him to maintain fires all across Thanatos. He's also able to teleport between any flames too, and that has been tapped to make him a kind of messenger.