Comic book example/subversion: Lucifer appears in The Sandman (1989), initially as a one-off villain, but later in the series, he grows tired of ruling Hell and being humanity's scapegoat ("How can anyone own a soul?") and resigns; Hell is then placed directly under "The Silver City"'s command.
Sandman formed the basis for his own series Lucifer a decade later, in which he's sort of but not quite an Anti-Hero. He appears as a blonde, handsome angel, with no hint of the demonic, except for bat wings — which he loses when he retires — and two tufts of hair intended to resemble horns. (He is referred to as "Satan" only once across both series, and that by a guy who wanted to make a Deal with the Devil and really didn't get it.)
Hellblazer: Satan and Lucifer are two different entities (as it was originally written in demonology [1]). Hell is run, after the departure of Lucifer, by Satan (known here as the First Of The Fallen). It is suggested that The First is the original Adversary, that he was created to hold God's own negative qualities and/or as a "best enemy" to God (as in some East European dualist mythologies) and that he knows some horrible secret about God, Jesus and the Church which, if confessed to a mortal, would send that mortal howling mad. John Constantine claims that he is God's former conscience. The First looks human, big and tough, wearing a dinner suit and cape, with a broken nose and long hair. He is addressed as "Lord Satan" by Gabriel on one occasion. John met the First while the devil was trying to collect the soul of one of John's friends. It didn't go well for the First.
The First of the Fallen initially shares his rule with the Second of the Three and the Third of the Three, who are similarly nasty. The Second appears as a living darkness, and the Third never appears as any one thing for long—he's a shapeshifter who constantly changes forms according to purpose, mood, or just for the fun of it, and it's implied he doesn't actually have a true form. They don't appear as often, though. Partly because they're killed shortly after they're introduced.
Several characters in The DCU are a good match for Mr. S. There's Neron, who ruled Hell for a while and, as the main villain of the Crisis CrossoverUnderworld Unleashed bought the souls of many supervillains, as well as killing the Rogues and Mongul to show how cool he is; Lord Satanus, who began as a human sorcerer yet grew powerful enough to kick Neron out; and his sister Blaze, who kicked him out in return. The most likely candidate to be the real deal is The Original Darkness, an Eldritch Abomination encountered by Swamp Thing, whose mere presence can kill several powerful sorcerers and whose fingernail couldn't be cracked by The Spectre. Finally, in the New 52 Lucifer appears as a villain in Demon Knights. In Batman RIP numerous characters imply or outright state that Simon Hurt is the Devil. Batman himself wonders this at the end. It is ultimately revealed that he is not.
There's a number of demons in Marvel Comics, most famously Mephisto, who have at one point or another claimed to be Satan. Fear Itself reveals that Satan—the real Satan, not the other demons who occasionally pretend to be him—has been missing for so long that many demons believe he never existed in the first place. The demons in the Marvel 'verse hold meetings around Satan's throne. None of them dare claim it for themselves, for fear of being torn apart by the others or worse, provoking Satan to return.
The real Lucifer (different from Satan) showed up in one Ghost Rider story claiming to be the one Johnny made a deal with and not Mephisto. He is one of several hell-lords, but unlike them cannot leave Hell on his own. He tricked Blaze into freeing him from hell to try and destroy the Earth, but quickly proved himself to be less then one hoped by being constantly outwitted by Blaze, who himself states he is something of an idiot.
The One Below All seems to be the ultimate evil in the Marvel Cosmos. Introduced in Immortal Hulk, his realm stretches under the entire multiverse and he uses a variant of the One Above All's description.
The Devil appears briefly in Preacher, where he is in charge of Hell and follows the stereotypical red-skinned, horned and hooved depiction. He is seen playing cards with the Angel of Death and is called Nick. When the to-be Saint of Killers freezes Hell with his hate, Nick attempts to whip the hatred out but fails. After the to-be Saint accepts his new role, Nick insults the Saint and gets a fatal round through the head for the effort.
Satan in the form of "El Diablo" pops up to show Johnny around Hell after his death in Johnny the Homicidal Maniac. Though he rules Hell, he doesn't seem to do much other than watch (with glee) the souls of the damned go about their superficial afterlives. He shows up again in Squee as the happy husband of an oblivious Catholic woman with whom he's fathered a son, Pepito. Pepito becomes the closest thing Squee has to a friend.
Another version of Satan shows up out of continuity in one of the Meanwhiles, where Jhonen, in an attempt to demonstrate how dissimilar his life is to Nny's after being accused of Author Avatar one to many times, shows us what an average day is for him. In a scene that (deliberately) mirrors an early JTHM issue, he arrives at a convenience store to get a slushy and picks a fight with the clerk. He then goads the clerk into admitting to be Satan, turns out to be correct, and blasts Satan with a laser when Satan threatens to bite his head off.
Jack Chick has put Satan into the Chick Tracts so often you'd think he was a regular. Satan, when shown, ends up being more of a general trickster than a real force of pure evil.
A demonic character shows up in Powers claiming to be the devil, but the protagonist is more inclined to thinking it's a minor demon trying to make itself seem bigger and more important than it really is. It's still a powerful, nasty, Hannibal Lecturing creature.
In Magnus, Lucifer is a literal Physical God who can be physically confronted and battled.
Satan is notably absent from the Hellboy universe, but he is finally mentioned in The Wild Hunt. It turns out he's been sleeping beneath the city of Pandemonium and Hellboy is destined to murder him and overthrow all his princes and generals.
A classic Strontium Dog story involved Johnny, Wulf, and the Gronk following a renegade Bounty Hunter named Fly's Eye's into a Hell-dimension, where they had to beat up Satan himself in order to escape. It turns out that Satan is actually a human who invented a device to enable travel between dimensions, but was horribly burned and scarred when an experiment went out of control. Shunned and rejected by the rest of humanity, he retreated to an empty universe shaped by his own will, and out of bitterness, he made it into a Fire and Brimstone Hell to torment anybody else who might wander in.
In Necrophim, Lucifer takes the form of a human with a forked tongue dressed in Edwardian English fashion. He mostly just wants to keep hold of his reign in Hell.
Anderson: Psi-Division: Judge Anderson once faced off with an nigh-omnipotent space-travelling entity which identified itself as Satan. After revealing its omnicidal harvests across the galaxy and its intent to destroy all life on Earth, it offered Anderson to join him as his herald. Satan was in fact borderline insane and lonely, and self-destructed when Anderson planted the seeds of doubt in him.
Appears in some stories by Wilhelm Busch, to take the (not so) pious Helene's soul to hell for example.
Spawn comics introduced Satan only briefly. He is the brother of God and was the original creator/ruler of Hell before being removed by his "Mother." God and Satan were two of a nearly infinite number of nigh-omnipotent beings created by the "true" God to help build worlds. They got Earth and, unwilling to share, fought over it, with God creating Heaven and Satan creating Hell, viewing humans as playthings in their wars. Out of disgust their Mother removed them from their thrones to try and give humanity a chance until Armageddon came. Both are evil, petty creatures. Ironically, Satan granted humans free will to spite God only for that to be what gives humanity the chance to free itself from both heaven and hell.
In the 24-issue limited series Crimson, Lucifer appears as a dapper blond man, handsome and wearing all white. He converses with God in a very cordial way and the two appear to have more of a "friendly rival" relationship. However, there are also undertones of Lucifer still wanting The Throne.
Black Moon Chronicles: Lucifer is a major character who rules over a Fire and Brimstone Hell and ultimately desires to have his Legions of Hell take over the Earth to turn it into his second kingdom. This first requires his ally and half-demon sonHaazheel Thorn to destroy the Empire of Lynn and cause God to leave the world in disgust with his chosen few. The prequel album, A Cruel Game, also reveals that the whole events of the series are the result of a Cosmic Chess Game that the Devil is playing with his chief lieutenant Pazuzu.
Hi Hi Puffy AmiYumi: "Dark Agent" shows the Devil as an entertainment manager who promises the girls wealth and fame beyond their wishes if they sign up with him, thus selling their souls to him. They reap the rewards of the deal but ennui soon sets in and they want their original manager Kaz back. Kaz challenges the Devil to a duel with Flying "V" guitars.
). Hell is run, after the departure of Lucifer, by Satan (known here as the First Of The Fallen). It is suggested that The First is the original Adversary, that he was created to hold God's own negative qualities and/or as a "best enemy" to God (as in some East European dualist mythologies) and that he knows some horrible secret about God, Jesus and the Church which, if confessed to a mortal, would send that mortal howling mad. John Constantine claims that he is God's former conscience. The First looks human, big and tough, wearing a dinner suit and cape, with a broken nose and long hair. He is addressed as "Lord Satan" by Gabriel on one occasion. John met the First while the devil was trying to collect the soul of one of John's friends. It didn't go well for the First.