The dorm leader of Maria†Holic, who rules with an iron fist and is The Dreaded among her students, is named God and for all she cares, you will think of her as such.
In Death Note, Light Yagami believes himself a god who brings his own form of justice to the world by killing criminals with a supernatural notebook (all thoughts that concern this usually being accompanied by Glowing Eyes of Doom in the anime). He proclaims his godhood in the first episode and is generally consistent in this. It's like an Action Prologue. Eventually, people also start worshipping him as one too, especially Teru Mikami, who always calls him "God." Near eventually calls him out on this:
"You yielded to the power of the shinigami and the notebook and confused yourself with a god."note A similar line is found in the earlier anime, Bubblegum Crisis.
Fist of the North Star is set in a post-apocalyptic wasteland where guns have ceased to exist. Martial arts masters who do not walk the path of righteousness will fall victim to this mental illness and proceed to build an empire of blood, tears and tyranny before being taken down by Kenshiro.
Neon Genesis Evangelion: Gendo Ikari, combining this goal with Love Makes You Evil (he wants to make himself and Yui God), and is more explicit at the God part in the manga. He fails at trying to become a Physical God, however. Shinji and Rei do succeed in it, but unwillingly. Also part of Yui's plan. Probably. Due to the nonsensical cosmology of this world, it's relatively easy for a Human to become any sort of God, since they already have one of the pieces needed. It just depends on how much of a God they become, and the ultimate version has potentially absolute control over reality, metaphysical concepts, and the ability to create new Universes at will. Maybe. We don't actually know, to be honest.
In Transformers Headmasters, Galvatron hatches a scheme to use the Earth as raw material to become a being akin to his creator, Unicron. When Punch, the Autobot spy learned of this plot, he uttered the words, "He's gone mad!" As if all of Galvatron's actions since the third season of the Generation 1 cartoon didn't clue us in already.
Kamichu! contains a noticeable aversion: The main character of the anime actually does become a god, for no particular reason, just before the series begins. She continues, however, to act like a confused, shy, somewhat overwhelmed middle-school girl, and her deific status is treated more or less like a part-time job. This is not so much a usual instance of A God Am I but more of an expression of the Shinto belief that all things and beings are tied to their gods.
Largo, of Bubblegum Crisis, not only considered himself a god, but developed a messiah complex for his Boomer "brethren" to boot.
Tenchi Muyo!: Kagato desires to acquire the power of the Juraian Royal Family and reign over the universe as its god. His name actually means "I am god who is man".
In Mobile Suit Gundam SEED, Rau Le Creuset, rants about him being the one to judge humanity which has done horrible deeds (especially in the last days and also to him. The whole concept is emphasized by his Providence Gundam as in divine providence. Though, it's not based on any god-like powers of his or the like.
His friend Durandal in the sequel Mobile Suit Gundam SEED Destinythinks of himself more as a High Priest (stated in series by Mu [maybe?]) of his new world order than a god.
Ribbons Almark of Gundam 00 believes himself to be far superior to any living being in existence, and feels that justifies his desire to conquer all of humanity. Then again, he is an Artificial Human.
Setsuna: Why are you doing this? Do you want to play God?
One of the trailers for the series release (in English, at least) even makes reference to this, using the line: "If you could change the world, would you be a god or a demon?"
The series itself seems to subvert this trope when it comes to Lelouch. As the series goes on, he fully embraces the image that he is The Devil incarnate, while the rest of world believes that he thinks of himself as a god. The title of the first episode, when translated without Bowdlerization involved, is "The Day the Devil Was Born". Better examples of this in the series include Schneizel (mentioned below) and to some extent, Charles and Marianne.
Lelouch's brother Schneizel develops a sudden god complex himself in episode 23 of R2, and ends up nearly killing Cornelia because of it. He intends to use Damocles' arsenal of FLEIJA nukes to rule the world by forced peace. Lelouch foils his plan and Geasses him to serve Zero.
In Air Gear, the Big Bad declares himself the King of the Sky after obtaining the Sky Regalia. Given the series' constant focus on having the freedom to fly however one wants, he's essentially declaring himself the lord of everything.
In Digimon Adventure 02, Ichijouji Ken (aka the Digimon Kaiser) has quite the streak of More than Mind Control-induced sociopathy. Considering himself superior to everyone else because of his genius, he goes so far as to declare himself the only individual worthy of entering the Digital World. Oh, and controlling it along with the actual Digimon, using Dark Rings. He pays for this. Big time.
Aizen has an extreme god complex, claiming that he alone can "stand in Heaven" and become something even a god could only wish to be. He even built a sky with artificial spying abilities and used the Hougyoku to try and break the boundary between the shinigami and the divine before Ichigo stopped him.
Second Espada Barragan proclaims himself the "God of Hueco Mundo". Eventually, he gets disintegrated by his own attack. His opponent notes that perhaps this is the only way to kill a god.
Yukio declared himself to be a god of his game dimension. Since Yukio's idea of fighting was based on video games and Hitsugaya was a seasoned warrior, Hitsugaya didn't have much trouble defeating him.
Yhwach, who claimed for himself the name of YHWH.
Mask de Masculine boasted that Renji would stand no chance against his "Godly" power. Renji shrugs off his attacks, impales him on his sword, and reduces him to a pile of ash.
Father, the main villain of the manga version of Fullmetal Alchemist, believes that humans are mere insects that are to be used as pawns in his plan. He's not human himself, being the original homunculus that all other homunculi comes from. His contempt shows when Ed goes to Xerxes, and discovers a transmutation circle that shows the name of God upside down.
In chapter 104, he uses the five sacrifices to force open the world's Gate, dragging God itself down to Earth and fusing with it.
Cars, the villain of the second part of JoJo's Bizarre Adventure, becomes "the perfect lifeform" just before the final battle. When you have absolutely no weaknesses and can feed on any living thing by touch, claiming godhood is not that much of a stretch.
GaoGaiGar, in its OVA, introduced Palparepa, a villain who believed that the "law of the material world" was that the victor was God and the loser was the Devil. He always saw himself as the god and GaoGaiGar as the demon, and the color schemes (GaoGaiGar was always black, Palparepa is a medical white) didn't help, giving him a distinct A God Am I variety of confidence in battle as well. After he's finally defeated, he goes out muttering "so this is the law of the material world...", seemingly acknowledging Guy as a god, albeit one of destruction (and subsequently, as the OVA strives to remind us, rebirth).
Shapiro Keats from Dancougar is always under the ambition that he will be a god. Which leads him to dump his lover Sara, and join the Muge Empire, rising up the ranks as a top-class strategist. Then his plans eventually come crashing down and he still held his delusions that he will be a god. This doesn't stop him from saving the Cyber Beast Force in "Blazing Epilogue" with his anger against the aliens who betrayed him. Dancougar is a machine fed by fury, and he had lots of it. All that frustration had to go somewhere.
Masami Eiri from Serial Experiments Lain: he commits suicide so he can enter the Wired and become its god, but he states that he's only able to be a god because he has followers, the hacker group known as the Knights of the Eastern Calculus. Eiri's ultimate goal is to connect all of humankind subconsciously through the Wired. That's what he created Lain to accomplish.
He's proven wrong quite dramatically at the end, where he actually does declare himself an "omnipotent god" before being interrupted by Lain. In a single Breaking Speech she hints at the existence of a real God, mocks Eiri for thinking himself anything more than a puny human and destroys him effortlessly when he tries to attack her in a rage. A God I'm Not...
He's declaring this to a girl who is omnipotent, omniscient and omnipresent. And probably immortal. Oh the irony...
Played straight and slightly subverted in One Piece. The villain of the Skypeia arc, Eneru, declares himself God. This is subverted in that, according to Gan Fall, the prior God of Skypeia, "God" is merely the title for the Skypeian leader. However, Eneru believes himself a true god by virtue of his lightning-based Devil Fruit abilities and power to read others' conscious thoughts.
And the fact that the word for god (kami) is similar to the word for thunder (kaminari) in Japanese. A fact he puns on by introducing himself with "Ore wa Kaminari" which can mean both 'I am Lightning' or 'I have become God'
Subverted in Magic Knight Rayearth: The Pillar of Cephiro has limitless power, as it is her will which gives shape to the world. When Hikaru achieves this state, in both anime and manga, she relinquishes it immediately and gives it willingly to the inhabitants of Cephiro, so they, rather than a single person, are responsible for their own world.
Miyo Takano, the Big Bad of Higurashi no Naku Koro ni. Their goal is stated at the end of Minagoroshi-hen to be "to become a god"; exactly what they mean is explored through their backstory in the beginning of Matsuribayashi-hen.
Big Bad: "Without a curse, there is no God. Because of the curse, there is fear. Because of fear, there is worship. Now is the time when God advents! I have become Oyashiro-sama!"
Keiichi too. In the arc where he tries to save Satoko from Teppei, he survives and thinks he has godly powers, because every person he wished to die died. The village doctor, a reporter, and Takano. However, it was a coincidence, and Takano actually went Faking the Dead. Not helped by the fact that the trauma of everything that's happened has caused him to snap.
Less seriously, in the first Visual Novel, everyone was playing a card game at the game club. Keiichi was winning almost every card game, and started calling himself a god. Even when it was four to one, Keichii was winning, and was mentally boasting the entire time. Hubris Ensured.
Takano's adoptive grandfather Hifumi Takano is a non-megalomaniacal version. He says that if he creates a lasting legacy through his research, then he will have become a god.
Pain, the leader of Akatsuki, thinks that his suffering has made him enlightened and his power made him God. It's not entirely unjustified. Though, it's worth noting he means more in a Shinto/Buddhist sense of a god rather than the omnipotent Christian one (in short, he doesn't have any illusions about being invincible).
Tobi is a bad boy. His ultimate goal is to essentially brainwash everyone by projecting himself into their minds and then setting himself up as a leader.
Black Zetsu verges on this, declaring boldly "I am the Land!"
Happens (arguably) to two characters in RahXephon. The first (and arguable) one is after Ayato fully awakens. The second is when Bahbem watches the tuning of the world. In Ayato's case, as he just merged with the RahXephon and REMADE THE WORLD, this isn't an unjustifiable assumption.
Creed from Black Cat does this after he uses nanomachines to become immortal. He tells Sephiria that her death will be the result of her opposing God (in other words, him). In a rather comedic moment, Creed explains to Train that he can recover from any life-threatening wound in a few seconds except for damage to the brain. Train promptly supplies that makes him more like a zombie, to which Creed angrily replies that it makes him a god.
Osamu Tezuka's Phoenix: volume Future, has main character Masato Yamanobe fill the role of God. Masato must begin the evolution of Earth anew when the current world is devastated by nuclear war (and it is hinted that this isn't the first time life on Earth has been obliterated). Masato doesn't want to be god and in fact tries to discourage the people he helps create from thinking of him in that way. The real god of the story is the eternal Phoenix, who gave Masato his power and immortality in the first place.
It turns out that Claire Stanfield's god complex is hereditary, as his great-grandaughter Claudia has much the same worldview.
Mirai Nikki has twelve already mentally unstable individuals empowered with precognitive diaries and made to battle each other; the winner will become God once the other 11 are dead. As a result, it's probably easier to state which one of the diary holders do not suffer from this to one degree or another.
The exact opposite also occurs: Dragon Ball features our green Namekian friend Kami. As you all know by now, that's Japanese for "god". Though he may be called a god, he has higher-ups in heaven and is infinitely weaker than all bad guys in Dragonball Z.
Dragon Ball Z: In the first Broly movie of the series, Broly is able to single-handedly beat down everyone. This includes (All of which are SSJ) Goku, Gohan, Trunks, and Vegeta. After Vegeta gets beat a second time, Piccolo appears to (at least try to) save the day. He looks at the damage, and then at Broly.
Piccolo: "What are you, some kind of monster?"
Broly: "Monster? No...I'm the Devil." (In the edited version this is replaced with "I AM A DEMON!")
Frieza shows vibes of this during his eventual Villainous Breakdown, completely unwilling to accept that he lost to a "monkey" such as Son Goku.
In Tengen Toppa Gurren Lagann this can be used to describe the power of those who have access to the higher levels of Spiral power. Lordgenome acts a lot in the fashion of a god-like king and the Anti-Spiral have taken such a position concerning the whole universe dedicating themselves to protecting it.
You can even argue that this trope regarding the heroes is subvertedanddefied at the end of the series. Simon could have ascended to god-status easily and permanently; at a certain point one might assume this will be the case, considering the amazing power he and Team Dai-Gurren have amassed. But instead, Simon refuses to take that role; Yoko and he even give the opposite of the "A God Am I" speech: "Simon isn't God, Gimmy." / "I'm just Simon the Digger." (He had his reasons, though it's a very controversial end.)
Yu-Gi-Oh! GX gives use several. Kagemaru wishes to harness the power of the Mythic Demons/Sacred Beasts to "become the God of the world" and restore his youth. Saiou, possessed by an Eldritch Abomination, wished to cleanse the world and remake it in "the image of light." Yubel wanted to fuse all twelve dimensions into one, and rule over them with Judai. Amon Garam wants to become the god of the alternate dimensions. Duelist of the week Frantz, who dueled using a copy of the Winged Dragon of Ra, merged with Ra using its special ability:
Frantz: Now you will respect me, you insignificant little insect! I don't have an Egyptian god, I AM ONE!
Rex Godwin in Yu-Gi-Oh 5Ds. He tries to Take a Third Option in the Signer vs Dark Signer war that has been going on for millennia by losing to a Dark Signer on purpose to become a Dark Signer himself, then grafts his brother's amputated arm with the fifth Signer mark onto his own stump of an arm. The end result is that he becomes a Signer and a Dark Signer at once, planning to use the Dark Signer's power to destroy the world, then use the Signer's power to remake the world in his own image.
ZONE in the most recent season is apparently also a "God of Destiny" ( being able to change the past and all that).
Director Kakuzawa in Elfen Lied wants to be the father of the future generations of the Diclonius race so that when it replaces humanity he'll be worshiped as their god. This doesn't work out well for him in the end, as it involved the cooperation of Lucy, who decided to kill him instead.
Moreover, his own status as a Diclonius turns out to be based on the racial myths of his once-persecuted, very Human family. Lucy's evolutionary offshoot has no connection to his clan whatsoever, as Lucy tells his corpse.
Played with, but ultimately averted in Ranma 1/2. The final Big Bad, King Saffron, is a Winged Humanoid with traits of The Phoenix — namely, he can fly, generate incredible heat (one of his attacks is named "Instant Empire Annihilation Blast"), regenerate, and resurrect himself after dying by turning into an egg and hatching as a baby version of himself. Although he has sufficient power he could conceivably be considered a deity (at least a kami), he is never referred to even by his human opponents as a god. Fanon, on the other hand, calls him a god all the time, presumably due to early fan translations. And then there's Rouge, who was Cursed with Awesome at Jusenkyo to transform into an Ashura version of herself. This gives her fire breath, lightning bolts, flight, and superhuman strength and endurance... additionally, an Ashura is also a literal god/demon of mythology.
In Berserk, Emperor Ganishka takes a stab at this, but Griffith really gets it done.
In the bloopers the voice over guy has a mental breakdown and becomes convinced that he is God when he finds out they've finished the last episode.
Theodore Dudek in King of RPGs wants everyone to play Role-Playing Games constantly. Yes, you guessed it... he wants to be the Game Master! Shesh's reaction and the last line illustrate this is a parody, but it's still a good example.
Theodore: Well, yeah... but it's sorta more then that. I want everyone on earth to play role-playing games constantly! To play them like breathing! Imagine a world where everyone is completely absorbed in their own fantasies! Better yet, my fantasies! I want to create an imaginary world that everyone dreams of being a part of! A grand illusion with me as the Game Master, adored by all! Games are about control! And when I have that control...I will reign over a new world!
Hardner from Rave Master. Interesting in that the ultimate Big Bad, Lucia, doesn't seem too concerned with anything godlike (sometimes). It's more like Lucia's Sinclaire wants him to have this sort of mentality.
Yuri subverts this near the end of the series. She discovers the source of the Shadow NPCs and is presented with the opportunity to effectively become God by taking control, but chooses to destroy the source instead.
In Psyren, the Big Bad Amagi Miroku claims to be "the god of a new world." Also, Usui who used his knowledge of the future to become God Emperor of Neo Amakusa.
Fairy Tail gives us the Exceed, a race who view themselves as this over the humans. Happy turns out to be part of this race.
In A Certain Magical Index, Accelerator certainly seems like this at first, as he claims he is trying to raise his power so that "even thinking of challenging me would be a sin," but it is later revealed that he had been convinced that becoming godlike would be the only way to prevent people from challenging him and getting horribly injured by his abilities.
Katekyo Hitman Reborn!: Byakuran can also be placed here, going as far as to kidnap Uni for her soul so he can activate the tre-ni-sette to create a new world under his rule.
Rosario + Vampire: Kamiya Kanade calls himself God. As a siren, he really did win the Superpower Lottery, but his delusions of godhood come to a crashing halt at the hands (or rather, voice) of Sun Otonashi, an even more powerful siren whose song causes his body to crumble to dust.
Yusuke Urameshi had a moment like this when it turned out that he's really anuber-powerfulYoukai, shouting "Kneel down and worship me, you insects!". Subverted in that he immediately reveals it to be an immature prank and says that they should have seen their faces. Which was itself a strong indication that he hadn't changed.
Played straight in the movie when the Big Bad declares himself a god.
Full Metal Panic!: Happens twice in the novels, after Kaname Chidori becomes possessed by Sophia, the original Whispered. The first time, in Semaru Nick of Time, just before Sophia takes over, she resonates with Kaname and she claims that: "If a God exists, then we are that existence. You are the entirety of the three Moirae. Clotho, Lachesis, Atropos." The second time it happens in the second part of Zutto Stand By Me, when Sophia/Kaname thinks that there is no God, no help coming from anywhere, only herself and the machine she had created to change the world.
"However, if the three Fates would be born from human technology, she would become all of them - Clotho, Lachesis and Atropos at the same time."
It's worth mentioning that most people loyal to Leonard Testarossa seem to think the same way about her, considering her and Leonard as Gods that would make their sad pasts go away, and give them a new, better life in return.
Yasako begins seeing herself as the goddess of the civilization growing on her face in one episode of Dennou Coil. It was...an odd episode.
InuYasha: When Rin was killed by wolves, Sesshoumaru decided to test Tenseiga's power by restoring her to life. When it worked, he concluded Inuyasha was a fool for having let him live, believing he now had no need to fear death. This is eventually lampshaded by his own mother who accuses him of thinking he had become a god and that he was very mistaken to believe he was immune to death. She proves this point by putting Sesshoumaru through Training from Hell against a foe that is immune to Tenseiga. Rin dies in the process for a second time, whereupon Sesshoumaru learns that Tenseiga can only ever revive a life once. Only when the truth about his god complex and the value of compassion sink in does his mother restore Rin back to life.
In Sword Art Online, the Big Bad Akihiko Kayaba's lifelong dream is to create a world that he himself has designed, with complete control over it. Fortunately, unlike many examples he simply creates a MMORPG to play around with. Unfortunately, he decides to trap 10,000 people inside that game, killing anyone who disconnects or dies in it, because otherwise it wouldn't be "real" enough for him.