In one particularly literal case, Dr. Doom tried to claim Thor's hammer to gain his power.
Doom is the unsurpassed master and monarch of this trope. "I want that power. By right, it is mine. For ultimate power is the ultimate destiny of Doom!" And, in fact, Victor von Doom has come within a fraction of a hair's width of securing Real Ultimate Power (TM) several times in the past. He has built a siphoning device that has allowed him to successfully steal not only the Power Cosmic of the Silver Surfer and Galactus but also The Beyonder's apparently omnipotent abilities in the course of the Secret Wars story arc, as well as that of a renegade watcher. Naturally, he is beaten in the end once again, but still...
After Mark Millar's run he gained god-like powers at a level strong enough to kill a Watcher. Still, it's possible that all writers will quickly forget about it.
In the Chaos Engine series of novels, Doom rebuilt the siphoning device and used it on Roma, Guardian of the Omniverse to try to claim her throne. The titual Chaos Engine itself was a (faulty) Cosmic Cube that granted Doom whatever he wished within its power- he used it to Take Over the World, rewrite history *
, and secretly use Mind Control on Magneto to make him into a genocidal monster to be his new Arch-Enemy (after he finally defeated that accursed Richards) because Victory Is Boring. He did not quite claim godhood...but, apart from making himself King of the Earth, he did think he had the right to kill everyone on the planet when he realised that the Cube was killing him.
Another X-ample with Apocalypse, who claims to have masqueraded as various gods during his millennia-long life. In the '90s cartoon, he delivers a great line to Graydon Creed: "I am as far beyond mutants as they are beyond you!"
And later, the returning Selene has made it very clear that she was now aiming straight at godhood. Well, not before making her enemies suffer and pay for having impeded her.
Wolverine narrowly avoided this during Lost in the Funhouse. After being imbued with the power of the issue's MacGuffin, he briefly revels in the thought of what he could do - before realising that if he starts using it, he'll never be able to stop and end up like the villain of the issue.
"I'm talkin' like God...only I ain't God. That was Horde's trip."
Hopping up on Chaos energy tends to do this to Echidnas in Archie Comics' Sonic the Hedgehog series; both Enerjak and his descendant Knuckles have attempted to warp reality to their own design after being supercharged by the Master Emerald.
In an alternate reality's future, Knuckles did succeed in altering the world as he saw fit, crushing all real resistance with ease and tearing out the souls of the most talented opponents (main cast included). However, in a twist of irony, he became so bored without a challenge he let the Freedom Fighters continue to exist for entertainment value.
And then, in an aversion of this trope, he has his power taken away and absorbed by his daughter, who doesn't let it go to her head, but instead intends to use the power to undo the damage Alt!Knuckles did before giving the power up.
Knuckles is almost the most susceptible to this trope, he fell into this again during his stint as Enerjak.
In a non-Echidna example: Feist is essentially God within the Special Zone, and anyone who goes there has no choice but to abide by his rules.
Batman villain Max Zeus is one of the 'so mad he thinks he's God' versions; although he doesn't possess any superpowers himself, he's managed to delude himself into believing that he is Zeus, All-Powerful Lord of Olympus. His last name doesn't help matters. Nor does his lightning cannon.
Zeus makes an appearance in the animated series but has a happy ending, of sorts. After being defeated by Batman (who he insists is Hades, since no mere mortal could best a god), he gets sent to Arkham. When he sees his cellmates "Hermes" (the Joker), "Janus" (Two-Face), and "Demeter" (Poison Ivy), he happily concludes he's reached Olympus at last.
Also, Ivy used the name "Dr. Demeter" in an earlier episode.
In Powers, 'The Sellouts' storyline revolves around a Captain Ersatz of Superman who has lost his mind and believes himself to be a god. The results aren't pretty.
Winnowill from ElfQuest has some very distinct ideas about The World How It Should Be - including her own unquestioned dominion over earth and space, and the non-existence of the main cast. Her Love Martyr Rayek suffers from the same malady, to a somewhat lesser extent (not that much lesser, though). He really goes over the top with it when he acquires the power of the Gliders' spirits, but once he arrives at the Palace they abandon him, leaving him (temporarily) a bit deflated.
In The Books of Magic, Timothy Hunter may become this in the future, and we catch glimpses of it. The first story arc of the series involves various magicians in The DCU trying to decide what to do about this.
Element Lad in the Legion of Super-Heroes storyline "Legion Lost." After getting lost through a time/space rift he transmutes himself into living mineral to survive, becoming immortal, and starts altering life on developing worlds to pass time, eventually creating whole civilizations of Scary Dogmatic Aliens. By the time his time-displaced friends find him again billions of years later, his powers have grown a thousandfold; he's lost all sense of morality and murders one of his former comrades on a whim.
During the end of Peter David's run on Marvel's Captain Marvel, Genis, the then-Captain, became Cosmically Aware and empowered. He was driven mad by being suddenly conscious of every event and being that existed throughout the universe at once, then subsequently went about erasing all of reality within a meager few pages. Reality gets better later, though. He later goes on to harass preachers and Asgard in an attempt to force his self-declared godhood on the rest of the world.
Ironically subverted during "The Korvac Saga" in The Avengers. Korvac, a supervillain, accidentally gains cosmic powers and knowledge... and, realizing humanity is at the mercy of uncaring cosmic beings, decides to help free the universe from them. Unfortunately, he is tracked down by The Avengers (who had no idea what had happened to him) and is exposed, ruining his plans. In the end, he commits suicide out of despair. This story has been retconned later to make it seem that Korvac was still villainous and that the Avengers were right in opposing him, but anybody who reads the original version can clearly tell that wasn't the case.
Even though (Depending on the Writer- originally and frequently, they really are) the New Gods aren't really gods per se, rather being highly advanced aliens, the New God Darkseid has always held himself to be a dark god in the flesh and is indeed worshiped as such by the people of Apokolips. He is the unquestioned ruler of his planet, has highly advanced powers and the only opponent who can stop him even temporarily is Superman. In the animated series, when Supes manages to beat Darkseid in battle, his followers pick him up and help him.
Swordsman: "You can't treat me like this! I'm a baron!"
Green Goblin: "I am God!"
The Skull of Earth X has the power to control the minds (or at least bodies) of every human being on Earth. Not surprisingly, he declares himself to be God. Ironically, he's more of a pawn of the "real" gods of the setting, the Celestial Host.
Skull: "You wouldn't even eat if I didn't remind you to. Fall down. You wouldn't bathe if I didn't get sick of your stink and make you. I'm God."
Mar-Vell gains omniscience in the sequel. Yeah, there you go.
A... different example was Snowflame from New Guardians, a villain whose power source was cocaine. After snorting a massive amount of it, he declares himself "a true god" — never mind that he has made it expressly clear that he worships cocaine itself as his god. But, then, cocaine and logic haven't always been the best of friends.
In some traditions there are deities or deity like beings that do worship the higher god in the pantheon. But yeah, a villain whose power source is a drug probably is just insane.
Hiro-Kala, teenage son of Hulk, gave us a really badass example, telling a whole army that:
Hiro-Kala:I am the chosen, progeny of Hulk the Green Scar and Caiera, shadow mother of all Sakaar. I am he of shadow, the life-bringer and world-breaker. Upon my planet I was known as Hiro-Kala. You will come to know me as GOD.
Rughal in The 99 attempted to become godlike by absorbing all the knowledge of the noor stones. It didn't end well.
In Sonic The Comic this happens twice to Robotnik. The first time, in the "Robotnik Reigns Supreme" storyline, he manages to absorb the power of the Chaos Emeralds and has reality completely at his whim until he gets outwitted by Sonic and drained of his powers. Much later he is hooked up to an alien machine supposed to drain the life force out of the planet and into his body, which gives him a brief moment of god-like powers until he is defeated again.
Toyed with in Watchmen, as, when Jon experiments with creating life, he becomes more god-like than most of the examples on this page, and yet he pointedly avoids thinking of himself in such terms.
In one two-part story in Captain America, the Red Skull obtains the Cosmic Cube and becomes this. He demonstrates by making himself a suit of golden armor and generating a Mook for Cap to fight. Eventually, Captain America knocks the Cube from the Skull's hand, and the Skull presumably dies diving into the water after it.
Borderline example: Evil Kryptonians like General Zod tend to see themselves as above everyone due to their incredible power. At least Zod is Genre Savvy enough to realize some people can threaten them, urging his Mooks to learn decent fighting skills and battle tactics.
In a Marvel UK Transformers Generation 1 story, Galvatron fits a massive energy collector to a volcano and keeps telling everyone present that as soon as he absorbs all the energy, he'll become a god. He fails, but just barely.
The Decepticon Sunstorm often does this because he's a Walking Wasteland, and he assumes this makes him unbeatable.
In Superman: Godfall, Lyla manages to drain a portion of Superman's power into herself, and she quickly goes to Metropolis and demands worship. She is quite surprised when the people don't comply.
Thankfully averted by Superman, who never thinks that his powers should grant him privilege and worship. Batman does note while observing Superman lifting up buildings that it's sometimes hard not to think of Clark as a god — and that people are very lucky that Clark never does.
It helps his case that Supes shares a setting with actual gods, many of whom are as far above him as he is above us, and as such could stomp his ass if he ever got too uppity. Exactly how far is Depending on the Writer, many of whom tend to treat Supes as a genuine god in denial.
A Chick Tract had one of these — an approximately 8-year old boy deciding he was a god after his mother explained to him the point of atheism — thus, he thought that if there is no god, he could become one. Straw Atheist? What else do you expect from Jack Chick?
The Scarlet Witch attained godlike powers for a time, which naturally proved highly detrimental to her sanity. Birthing children with an android probably didn't help.
In Action Comics, Lex Luthor merges with a Phantom Zone entity and becomes a massive godlike Energy Being. He uses his new power to halt entropy in all of existence and grants everyone immortality and eternal bliss while reveling in his godhood and flaunting it in the face of Superman. Then his Loisbot informs him that the zone entity made sure Luthor couldn't do anything negative with that power such as killing Superman. He can't refrain from trying, and so squanders his power in self-destructive pettiness.
Doctor Destiny from The Sandman when he briefly acquires one of Morpheus' artifacts. He actually does manage to cause mass chaos in both the real world and the dream world, and almost destroys the dream world entirely... until he accidentally gave the Lord Of Dreams a Power-Up.
There's a curious heroic version of this trope in the final Eighth Doctor comic strip in Doctor Who Magazine; the Doctor merges with the space-time vortex in order to defeat the Cybermen, becoming a being of practically godlike omnipotence in the process. Although he remains benevolent, his omnipotence distracts him; he's so enthused about how he can see everything and feel everything that he doesn't notice that his companion remains on the Cybermen's rapidly decaying space ship and is about to fall to her death. Then, as the Doctor's about to say goodbye to her forever, he notices her about to fall to her death... and instantly gives up godhood without a second thought so that he can catch her before she falls.
In The Boys, the Homelander develops this mindset after being driven insane by pictures of himself actually his clone Black Noir dressed up as him committing horrific crimes like baby eating and rape, crimes that he didn't remember committing.
The First in CrossGen comics ("We call ourselves the First, but you would call us gods."). Somewhat justified in the fact that they really do possess godlike powers and a murky sense of their own origins that leads them to believe that they created the universe. Their actual creator Solusandra also adopts this attitude sometimes, or even flat-out declares herself above gods (having created a lot of them after all).
The first is Xadhoom, who became a Physical Goddess (she has basically the same powers as Doctor Manhattan minus the ability to see the future, and a lot more firepower) in the attempt to find an eternal energy source for her homeworld of Xerba (then on the verge of an energetic crisis due their sun slowly dying) and makes clear she has no reason to return normal before performing her Heroic Sacrifice and an improvised stint as The Chessmaster that will start legends of her as a vengeful goddess ready to show up every time the surviving Evronians do anything funny.