A character that is all-powerful. Either literally omnipotent, or are simply so powerful that they're virtually omnipotent within the context of the story. In fact, there's a sliding scale of sorts to measure how powerful a being can be.
It can go one of five ways, at least in fiction.
The character has absolute omnipotence. As in, nothing can challenge them, and they can literally do anything and everything, logic and causality be damned.
The character is omnipotent. They can break logic and causality to achieve anything, but there are others who can do this as well (sometimes they're The Anti-God). What happens if they go against each other can be a massive Mind Screw.
The character can do just about anything that's logically possible (i.e. virtual omnipotence), or at least appear to, thus making sure Magic A Is Magic A in the process. This type of omnipotence is also more frequent than the above type to have multiple characters that operate at this level. The term nigh-omnipotent is often thrown about at this level.
The character is omnipotent within a field or concept. Specialized omnipotence, if you will. Anthropomorphic Personifications are almost guaranteed to display this with the concept they embody.
The character is "merely" an almighty being, whose power is far beyond any other in the setting. For practical purposes though, they're basically omnipotent.
The most powerful Reality Warpers tend to exhibit this. Combine this with a strong Ego, and you get A God Am I (which may or not be completely true). Combine it with Cloudcuckoolander tendencies, and you may have a Great Gazoo, or worse, a Mad God.
Because of their powers, omnipotent characters are usually totally invulnerable to anything. Nigh Invulnerable by contrast is a step lower than this. Complete Immortality is also very common.
Compare The Omniscient, who often, but not always, overlaps with The Omnipotent. Cosmic Beings are often omnipotent as well. If they don't actually do anything, they're an All-Powerful Bystander.
Examples
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Anime and Manga
Dragon Ball has the dragon Shenron, who can grant nearly any wish. The dragon of planet Namek is apparently even more powerful. The few restrictions seem to be put in place by the creators of the dragon balls as safeguards. Dragon Ball GT has the black star Shenron, who has no limits.
Subverted in that Shenron was destroyed, and not by one of the end-of-series villains either.
Jack Rakan of Mahou Sensei Negima! fits to an extent, seeing as how he can do things that fly right in the face of logic and magical theory.
There are at least three beings as strong or stronger than him (Nagi, Evangeline, and Lifemaker), but Rakan fits this trope the most because of how he usehispowers.
From Kara no Kyoukai, Ryougi Shiki's Third Personality is an Anthropomorphic Personification of the Root of Creation, and, much like Haruhi, is capable of destroying the universe and replacing it with a new one on a whim.
In Tenchi Muyo! we have The three Choushin: Tsunami, Tokimi, Washuu, and Misaki as type 2, and Tenchi himself as type 1, though not manifested as such yet. Z and Ryoko at full power are arguably type 3. The Zinv and current Tenchi are type 5, as are the most powerful Jurai trees.
In Medaka Box Ajimu Najimi is functionally omnipotent, in that she can do anything including changing the laws of reality, but feels bound by the Theory of Narrative Causality which prevents her from ever winning against a "main character".
Hao Asakura has become the lowest example of this in Shaman King before the heroes even meet him. His control over reincarnation, connection to the Spirit of Fire, and centuries of experience mean he's unbeatable from the get-go, with the next-best shamans being as nothing in comparison to his power. In a setting where resurrecting a dead person is possible, if draining, for the very powerful, Hao can perform mass resurrections after single-handedly defeating a human navy supplemented by powerful shamans. The plan to defeat Hao is to let him win the tournament and gang up on him with the five Olympus Mons elemental spirits while he can't fight back, but the heroes admit even this is fairly unlikely to work. When Hao awakens as Shaman King, he's omnipotent and kills the entire cast with a thought as he prepares to reshape the world to better please himself; fortunately, Yoh expected something like this would happen when he realized even if they were strong enough to win, the heroes would never be able to end the threat Hao presents with violence. Instead, the entire cast appears within Hao's mind and manage to avert the extinction of ordinary humans by reasoning with Hao instead of trying to overpower him.
Comicbooks
The titular character from Enigma is what happens if God was gay, morally ambiguous, and ate lizards. It's kind of a weird comic that way.
The Beyonder from Marvel Superheroes Secret Wars and Secret Wars II. The living embodiment of a universe, can do or make anything it wants - but it doesn't understand the concept of "wanting."
The Spectre and Captain Atom, as they are vastly powerful, much more so than even Silver Age Superman.
Only some of the times, both characters yo-yo up and the down the power scale. For example the Captain Atom/Wildstorm miniseries showed that Captain Atom isn't so much omnipotent (travelling back in time to an event only recently past was such a drain on Atom that he could only do it once a week) as his enemies were dropping idiot balls like mad (Wildstorm's most powerful person Jenny Quantum, rather than warp reality or shoot him with a quantum beam, she reached out to grab Captain Atom who's beginning to go into meltdown and got fried for her "effort").
As for The Spectre, he is the living embodiment / agent of the Wrath of God and his power depends on how much God decides to let him use on any given day. At his peak though he is the strongest character in the entire Verse bar God himself. In various company crossovers, he is said to be the DC counterpart to Marvel's Living Tribunal, who is canonically the second most powerful being in his multiverse and subordinate only to God himself.
Trigon from Teen Titans claims to be this, as well as omniscient.
Which is BS. DC's true omnipotent is God aka The Presence. Trigon was later retconned to be the Anthropomorphic Personification not of All Evil in the DC-verse (as he was originally), but of All Evil of one particular magical dimension. In either case, for all his incredible power, there have always been several other heroes and villains who had better hype and feats. The Anti-Monitor comes to mind, a universal-scale Reality Warper who drew power from destroying entire universes and did just that several times over, and at his peak was strong enough to take on even The Spectre in one of the latters stronger showing.
In Marvel, a supposed characteristic of the One Above All, who is also hinted to be the capital-G God. The most powerful entity stated that appears, the Living Tribunal, seems like this compared to the protagonists but it can't act without all three of its heads in agreement. So it usually does nothing.
The DC Presence is, or was, occasionally referred to as The One Above All by some, including The Spectre. This was a probably deliberate hint that the Marvel and DC God are actually the same being. In other words, He is the most powerful comic book character period. Assuming He isn't simply code for "the writers".
Also, The Presence is the same being as The Source from the New Gods (probably), as both are aspects of the same all-powerful being. Other aspects exist (eg. The Voice), but they are mentioned far less often.
A pair of supposed omnipotent entities in the Marvel Universe once got into a debate over this when they ran into the the Celestials. One of them didn't understand why the other was so intimidated by the Celestials because they were both omnipotent and nothing should be able to threaten them; the other told her that yes, they were omnipotent, but there are "levels of omnipotence" and the Celestials are on a much higher level than either of them.
Man of Miracles or M.O.M. for short in the Image Universe, or at least in Spawn, s/he is also Kali and Jesus Christ, and God of the Old Testament is just his/hers son.
Superman Prime is Stated to be the second strongest being in the entire DC Multiverse, next to The Presence itself.
The Ellimist and Crayak from Animorphs both have unlimited power, and regularly cause the creation or destruction of species. While they agreed to no direct interference as part of their "game," neither of them fit the All-Powerful Bystander trope - they both are skilled enough at manipulation to still cause massive changes in the history of the galaxy.
Happens at the very end of Brain Jack by Brian Falkner. Sam ends up merging with the A.I. Ursula and gaining the ability to control everything and know almost everything as well, because in this future, Everything Is Online.
In Heir to the Stars: Overture by Lionel Suggs, there are more than a few of these types of beings in the story. There are several of characters that are the Be-All, End-All of levels of existence. In the very opening, it states They are defined as the Be - All, End - All of the perpetual, unchanging, unbounded, immanent, and transcendent truth, which are the existences and principles behind the Divine Ground of all matter, energy, time, change, action, necessity, fate, destiny, reality, space, being, actuality, potentiality, possibility, nothing, the active principle behind the phenomena of the absolute infinite and imagination, and everything above, beyond, and outside a system of everything beyond The Mainfold. It even goes in to explain that there beings known as Overtures and Finales. An Overture and a Finale can do anything they supremely well please because they are the Grand Principle behind the infinitely All-powerful, THE ALL, any and all systems, as well as any and all states; encompassing all meanings of Omnipresence, Omniscience, and Omnipotence..
Nobody in Starfleet possesses Complete Immortality, apparent omniscience, or the ability to warp reality with a click of their fingers, so that's being a little overly modest. Unlike Starfleet, their powers are not dependant almost solely on technology, and are inherent to themselves. The only known limit to their powers is the rest of the Continuum, who can collectively impose punishments like removing their powers (though they still know almost everything), imprison them or make them mortal. That and a Patrick Stewart Speech.
Also the Dowd, a being who casually exterminated an entire race in a moment of anger. Probably a type 2 or 3, he wiped out said race in an instant with damaging their ships, and while he can simulate life, he does not appear to be able to time travel or to truly revive the dead.
The EU novels have 0, a former friend of Q who is arguably more powerful than Q, but in the past was crippled to not be able to travel in time or faster than the speed of light.
Tabletop Games
Nobilis: type 4. Nobles can do virtually anything within the confines of their Estate, especially if they invested heavily in Domain and Persona, which govern (respectively) your control over the raw material of your Estate, and your control over the little "[Estate]ness" dial on everything else in the world.
In The Bible, St Paul claims that God can do anything that is logically possible (while still possessing absolute supernatural power), but cannot do things that are mutually exclusive, like making a stone so big even He can't lift it. How far St Paul is an authority on the nature of God, or is just stating what he believes to be true (or just trying to pre-empt/diffuse these kind of arguments), is up in the air.
This is generally the position taken by some Christian theologians and philosophers such as St Augustine or St Thomas Aquinas- God can do anything, except that which makes God "not God", so He cannot do something that removes or defies His omnipotence, including simply making himself not omnipotent (since one paradox is that an omnipotent being can make himself powerless, but still be omnipotent, since he is omnipotent- these philosophers say that He can't, thus removing the paradox). For Augustine, this is because God is perfectly rational, and is also perfect, and being perfect would not act contrary to His nature, which is to be rational, and since such paradoxes are irrational He can't do them. In other words, the question is regarded as fallacious and nonsensical, and just a trick of word play.
On the flip side, other Christian philosophers like Rene Descartes say that God can do absolutely anything, reasoning that He existed a priori to logic and is the one who tells logic what it is. The only reason such paradoxes exist is because logic acts a certain way from a human perspective, but the level of God is one humans cannot comprehend and what are apparent logical paradoxes to us are not so to God. This is called Absolute Omnipotence.
Genies. Most mythologies/folk tales about them indicate the only restriction is that they are bound to their lamp/jar/whatever, and must obey the one who frees them (and this gets subverted sometimes). Some works add rules for plot convenience like Aladdin, but generally a genie = Phenomenal cosmic power, itty bitty living space.
In folk tales and other fiction, they seem to be omnipotent. In mythology, however, they're supposed to be able to do many things humans can't, but also unable to do many things humans can, and often aren't bound to lamps or anything else.
Averted by most Polytheistic pantheons, since even the Gods are subject to fate.
Video Games
Asura's Wrath plays around with this: Chakravartin is referred to as the Omnipotent Ruler of Gaea. However, he's eventually defeated by Asura.
Umineko no Naku Koro ni has Featherine AugustusAurora, who is perfectly capable of pausing the plot of the visual novel she's in, deciding she wants a scene to play out a different way, and rewriting the script of the novel itself. The one 'fight' we see her take part in, she decides she can't be bothered to think of a fight scene at that moment, so writes down that Lambdadelta gets defeated by [Blank Space], saying she'll fill it in later. This results in Lambdadelta being killed by nothing, out of nowhere, instantly. The character who got one-shotted was laughingly throwing and tanking big bangs, and had, up until that point, been the tied-for-most-powerful character in the whole story.
Webcomics
minus. is about a seemingly omnipotent child, who mostly uses her power as a toy.
All of the Author characters in Bob and George have god like powers. Seeing as how The Author is the creator of the comic universe he IS a god there. The Helmeted Author is apparently an Author of a different universe and the Shadowy Author claims to be one at first and ultimately turns out to be a future version of the actual Author.
In Homestuck, every First Guardian is omnipotent, and can also be omniscient as well depending on what they were made with. Other characters are not First Guardians but gain their powers for themselves. Abilities shown so far:
God-Tier Jade: teleportation, size manipulation (the latter may come from her powers as the Witch of Space, but on the other hand Becquerel was briefly shown using that ability as well.)
PM: None yet, but presumably at least teleportation.
Schlock Mercenary: A certain AI named Petey (who was already insanely smart, and already controlled a huge fleet of warships) manages to take over a power generator made out of the Galactic Core! Except for the Pa'anuri, there is practically no one who can fight him... or even last three minutes against his moderate dislike.
Web Original
One of the terms coined by the Spacebattles forums is "ROB," or Random Omnipotent Being. A ROB is used to justify ridiculous scenarios, or create events for people to talk about. A ROB is usually used as a Deus Ex Machina for a random event to set the plot moving in a quest.
In Funny Business, Jeannette has no limits on her power. Lewis takes advantage of this to solve the omnipotence paradox.
Western Animation
In a dream sequence of a Halloween episode of The Simpsons, Bart is an omnipotent boy who freely changes things about him for his own amusement. Bart eventually wakes up with a scream when, in the dream, he actually reconciles with Homer.
Amazo after his/its return in Justice League Unlimited has learned or copied the superpowers of every entity in the universe. The only power he lacks is imagination to find a purpose for all his powers. That's why he is coming after Lex Luthor, his surrogate father-figure, next. However, Chaos Magic is something he cannot deal with, as it can absorb his attacks- he left the Earth in fear when he found this out, to figure out a way to counter it....and as far as we know, he is still doing just that dozens of episodes later by the time of the Grand Finale. A little embarassing really, since the League solved the problem themselves a few minutes after he left.
Discord of My Little Pony: Friendship Is Magic appears to have a number of incomprehensible abilities (such as creating interchangeable days and nights, chocolate rain, and soapy sidewalks) which he puts to use in creating utter chaosthroughout Equestria. Basically the only rule seems to be that he can do whatever he wills - fitting, as he's voiced by John De Lancie, who plays Q in Star Trek (as noted above). He even snaps his fingers to work his magic, and with the same sound effect when things do happen. The only thing more powerful than him seems to be the the Elementsof Harmony.
Which makes sense, if you think about how he and the Elements represent opposing forces that CANNOT, by definition, exist without the other. He identifies himself as the "spirit of chaos"; that is, Chaos Incarnate. If the Elements destroyed him, there would be no chaos by which to define harmony.
