Happens a lot in the anime .hack//Roots. Fights are left offscreen apparently due to low budget. For example in episode 6 only bit of action we see is a funny angle in which Enders repeatedly kicks Haseo. Episode 23 has Haseo fighting against one hundred players in one episode and viewer sees almost nothing since it focuses on Haseo's teammates. Other disappointing fights include Ovan vs. Tri-Edge and Haseo vs. Tri-Edge whose climaxes are omitted.
The special Pokemon Mewtwo Returns: Team Rocket, led by the rarely used Giovanni, have captured the Pokemon clones and their babies. Mewtwo is horribly injured, and Ash must free the Pokemon and help Mewtwo. When Giovanni and a small army of TR grunts shows up to fight, Misty and Brock step up to fight, letting out their Pokemon. Then it cuts away to a different scene. When it cuts back, the battle's over, thereby skipping one of the few battles against the Team Rocket organization as a whole (not just individual members like Jessie and James) in the show's entire 14-plus season history.
In the main series, May's final battle in the Kanto Grand Festival. It's a staple of the anime in the later sagas to have two rivals in the tournament arcs - one for the protagonist to beat, and one to beat them. After May's epic battle with Drew - which started at the tail end of one episode and carried on into the bulk of the next - we only see the last two minutes or so of her battle with Solidad.
Ash's Quilava's battle against Nando's Armaldo in the Sinnoh League tournament. The second that Ash sends out his Quilava to battle, the scene shifts over to the Team Rocket trio trying to make sales with their merchandise. By the time that it gets back to the fight, both Pokémon are on the ropes and do one final attack on one another only to double-KO each other.
Also, during the Johto League, Ash and the gang encounter a witch who miscasts a Pokemon translation spell, turning Ash into a Pikachu at the end of the episode. The transformation is stated to last a few days, and the next episode picks up... about five seconds before it wears off.
Devil May Cry: The Animated Series: in the final episode, Dante finally pulls out his Devil Trigger Super Mode...Offscreen. He's grappling with the Big Bad, the camera zooms in on his face, he starts glowing, his eyes widen and his voice deepens. The camera cuts back to show an explosion on the roof they are fighting on. When it comes back to them, the fight's already over (though this also holds the implication that he may have used devil trigger explosion and killed the demon instantly with that).
Black Butler emulates Devil May Cry as Sebastian reveals his true form in the first season finale to fight. We never get to see it kicking asses.
Midway through Blood+, Saya confronts Diva face to face after Diva has rampaged through the good guy's base of operations, killing dozens of mooks and raping and killing Saya's younger brother Riku in the process. The episode ends with Saya and Diva sizing each other up in preparation for a no-holds-barred beatdown. The next episode...starts with a one-year Time Skip and follows the supporting cast as they struggle against Chiropterans in the U.K.. Saya show up by episode's end, of course, but the big fight is never mentioned again, not even when the two characters fight for real later on. Also in the same episode Riku was killed on the verge of Taking a Level in Badass, though this is much more defensible dramatically and indeed becomes crucial later on.
The first season of Code Geass ended on a massive cliffhanger with several characters' fates hanging in the balance. But Executive Meddling forced the second season to start with a Time Skip and a reboot, after which part of the season was spent on a retread of season one's plot. To their credit, the writers tied up most of the dangling plot threads eventually via flashbacks, but the end result was rather anticlimactic.
Also, in R2 Turn 22, after the epic showdown with Lelouch's parents, Suzaku finally confronts Lelouchand the two are about to speak honestly with eachother. Keep in mind their love-hate relationship has been the driving conflict in the show.The narrative cuts to a month later, with Lelouch and Suzaku's alliance having formed off-screen. Now, it makes sense for narrative reasons, but it still feels anticlimatic.
Kare Kano's abrupt The Resolution Will Not Be Televised ending, especially since we were getting all hyped up about the play Yukino had been preparing for the past few episodes. This is made even more unforgivable by the fact that, after religiously following the manga virtually to the panel for almost its entire length, Gainax diverted from the story to add an original filler episode just before the end, when only one more episode would have allowed them to portray the play in its entirety.
Bleach hinted at a battle between Head Captain Yamamoto and Captains Kyoraku and Ukitake, two of the more powerful Soul Reaper captains. After the three release their zanpakutos, we never see the fight again until they call it off after Aizen's treachery is revealed.
Bleach manages to use this twice in the same battle, between Rukia and Rudobon, thanks largely to being overshadowed by another fight taking place at the same time.
So Rukia, Renji, and Chad are confronting Yammy. They're thinking they can take him, since all three of them have fought stronger Espada than him and lived to tell about it. Then he releases his sword, turns into a giant dinosaur-man who towers over them, and reveals that he isn't the 10th Espada, he's the 0th Espada, the strongest of the bunch. Oh, man, whether you think that's a good plot twist or not, it just has to lead to an epic fight, right? Then, just as this fight begins...the viewpoint cuts away to other battles. For several months. And when it comes back to them, Yammy has already won. Easily. Off-screen.
The past two examples are somewhat averted in the anime, which extends/shows parts of both fights.
Byakuya and Kenpachi are setting up to fight Yammy, Espada 0, at his full strength. The scene cuts away to Karakura town, and the war with Aizen. More than fifty chapters later, we see that they won off-screen, and Yammy is left dying in Hueco Mundo. Even the anime didn't do much to extend the fight.
In the Zanpakutou Tales Filler Arc, Kenpachi is facing down Tengen, Komamura's Zanpakutou, whose Bankai is basically just him transforming into a 60 foot giant. Giant!Tengen smacks Kenpachi around, Kenny declares he's going to get really serious, then...nothing. Tengen later appears, fully tamed at Komamura's disposal, at the arc's climax. A similar issue happens with Yoruichi's fight with Haineko and Tobiume, though more of that fight was shown overall.
The fight between Kensei and Wonderweiss has the same problem. Although we know that Wonderweiss won, it isn't shown how at all. Kensei just kind of disappears.
Kensei reappeared more than two years later, reinstated as a captain after the time skip...although we still don't know the results of that battle, beyond that Wonderweiss escaped.
Kenpachi does this again in the Vandenreich arc - while superpowered enemies are killing everyone in Soul Society, he casually shows up carrying three of their corpses over his shoulder. Bonus points for describing their powers (turning into a giant ape with a sonic roar, turning into an exact copy of the opponent, and... he's not sure what the last girl could do, because she kept trying to explain her powersinstead of defending herself, and Kenpachi was still deaf from the sonic roar).
The manga once again uses this intentionally for comedy, once again involving Jack Rakan. four of Fate's minions go into their One-Winged Angel forms to fight him. Then this happens. If any other character tried to pull that, it would be a huge cop-out, but in this case it's perfectly in character for Jack, and preserved the minions' abilities for more dramatic reveals in later battles against the main characters.
Also can't forget the massive 3rd day of the Mahora Festival and the climactic battle against Chao Lingshen's forces. One part of the battle involved Kaede going up against Mana. Easily two of strongest characters in the series even now, and we only get to see the first part of the battle and the result (the two hit each other with time-displacement bullets at the same time, rendering the match a draw).
The Setsuna/Tsukuyomi fight in the climax of the Magica Mundus arc. Here we have Setsuna getting a rematch against an opponent that not only defeated her earlier but also implied that she'd rape Setsuna, or something to that nature. This time Setsuna is armed with a renewed self-confidence and a new pactio forged by her fandom-pleasing make-out session with Konoka while Tsukuyomi uses some kind of demonic power up of her own. The fight starts, it's good and then it just kind of jumps to the end. We're told that they fought for over half an hour, but we're only shown like a third of that. Good build-up that lead to a rather hollow climax because we didn't get to see the stuff that lead up to it.
The finale of the entire series did this with the climax of the Myth Arc of the entire series, which had apparently been resolved off-screen with the Lifemaker apparently having been beaten and Nagi apparently having been saved in an apparently epic battle that apparently showed how powerful Negi and his entire class were when they were all united.
The Nine Tailed-Beasts, almost all of which are fought and captured offscreen. When it was revealed one of these characters had control over lava, many fans were crushed that such important characters were treated like forgettable Mooks. The fillers expand on at least one of the Jinchuriki, but much is left to the imagination.
Another particularly egregious example would be Kakashi's battle against the remaining zombified Seven Swordsmen of the Mist. Fans were looking forward to seeing him "go on a rampage" and finally offset the massive Worf Effect that he'd accumulated. Indeed it is implied to be an absolute Curb-Stomp Battle in his favor, but the battle occurred entirely off-panel.
Fortunately, the anime team was well aware of Kishimoto's choice to omit the battle and gives us a generous Adaptation Expansion, showing a full and proper fight. As we all know, it was probably because a.) fans would've pissed on the animation studio doorstep if they tried to skate around showing the battles, too, and b.) to provide some padding so that the anime wouldn't lap the manga - one filler marathon run was bad enough.
The most egregious example of all may just be Tenten fighting Kakuzu with the Bashosen - a war fan that drains an immense level of chakra, but in return, can create a vast amount of a specific element. Being a weapons specialist, and getting some slight screen time (which compares normally to how she gets less panels than a landmark, the Hokage mountain) you'd expect a full out fight for the ages coming up, right? Wrong! Instead we see Tenten passed out, face down in the dirt as a medic tells her never to touch the fan again while the panel just before showed two of the three masks broken (Asuma destroyed the other one). Kishimoto teases us again later, implying she's planning something with Team 10 but that'll never be revealed either.
That aforementioned wrong becomes a "Right" in the anime. We get to watch Tenten destroy both masks - one right after she obtains the Bashosen, and then again after several episodes when sunset is approaching and she's heavily tuckered out from hours in battle. Yay, Adaptation Expansion!
Itachi blackmailing Danzo Shimura. Who doesn't want to see how that went down?
Five Kages off-panelled by Madara. 'Nuff said. In this case, it's Played for Drama and shock potential, as, it was made perfectly clear that they didn't stand a chance in hell.
In MADtv, a female student even points this out in a parody episode called Naru210. The cameraman apologizes, admitting he is easily distracted. So of course when he focuses back on Naruto's fight again, it's already over.
In the YuYu Hakusho manga, the Demon World Unification tournament sets up some potentially epic battles (Kurama vs. Shigure, Hiei vs. Mukuro, Yusuke vs. Yomi), but only shows a little of Yusuke vs. Yomi before suddenly cutting to after the tournament.
In Canaan, it is never shown how Yunyun saves Maria from being blown up by the time bomb in that train car. That must have been quite a stunt, especially considering how little time she had to pull it off.
Outlaw Star gets very lazy with many fights, cutting away from the action at bad moments. The second to last episode in particular totally skips two apparently awesome fights: Suzuka's finishing attack was shown as flashes of light in her eyes, and Aisha's frenzied assault in beast form was totally obscured by a whirlwind.
The last one at least has an explanation that the whirlwind was an "ultimate attack" type dealy, which nobody had ever survived before. The bad-assery is that Aisha transformed, jumped in, won, and seemed no worse for the wear. Doesn't change the fact that the whole thing was over very quickly and without detail.
The ending of Sailor Moon S skips Sailor Moon and Sailor Saturn's fight against Pharoah 90. We even get to hear some of it, but it all takes place inside an opaque dome of energy so nothing is seen. This is also the closest Saturn really gets to doing anything in the series.
Also between episode 5 and 6, the three girls have their first battle against a major villain (Circulas) and it just started in the end of episode 5. The battle was completely skipped in the following episode, and both sides were fine and didn't have any signifant looses.
In the One Piece Marineford arc. Several times throughout the arc, two fighters meet and start to exchange blows in a page or so. Then the scene changes, and when we see the two fighters again, the fight has stopped without any further explanation. Sort of Justified, though, in that you don't really have the time to fight a one-on-one battle in a massive war with all the opponents to be concerned about.
Several epic battles take place off-screen. Some examples include Garp and Sengoku vs. Shiki, the Red Hair Pirates vs. Kaido's crew, and for the title of the new Fleet Admiral post-Time Skip, Aokiji vs. Akainu... we'll see it all in due time, right Oda? Right?!
Katanagatari episode four had an intentional example, and spent a large part of the end of the episode rubbing it in viewers' faces: Shichika barely manages to defeat the mysterious white-haired badass the show had been building up for the past three episodes, thanks to Togame drafting him a brilliant strategy. Or so we hear, at length, from the two afterwards. The audience spends the majority of the episode with his sister, on an island miles away.
Preview at the end of episode 3 involves parting the sea, slicing up rocks, exploding a whole island, and fighting a giant shark.
One episode of Yu-Gi-Oh! GX had the captain of a submarine offer the series' main character the chance to work with him and travel the world. When our hero refuse despite the very generous pay, the captain forces the matter by saying that if he doesn't win their duel, he'll have to come with him. Jaden soundly defeats him, and thus has no actual obligation to take up his offer, but the captain persists and tricks Jaden's friends into leaving him behind. The episode immediately cuts to several weeks later, with Jaden's best friend brooding over the fact that he left. Jaden then comes in, battered and bruised, after having fought his way to freedom. Needless to say, his friends were overjoyed.
In the manga, Jaden/Judai also defeats Crowler/Chronos as part of his entrance exam, but it's never shown, despite being referred to a few times.
The Anime's Ending with the duel of Yugi and Judai, after Yugi turns into Yami He proceeds to summon Slifer and Judai proceeds to attack him and the screen fades to white and then skips ahead to a unspecific time afterwards, the end of the duel is left ambiguous as and also leaves out how the hell Judai get back to his time, not to mention how he ended up in the desert.
The ending of Bio Broly in Dragon Ball GT. Goku was apparently supposed to fight Broly in Hell due to the latter acting up for some unknown reason. The movie ended while Goku was going back to filling his stomach in preparation, and they never show the fight, as it ends right there. There's not even a reference to it in the next three movies, despite the immediate next movie dealing a lot about Hell and the Afterworld, namely it mingling with the mortal world.
In Yellow Dragon ga Arawareta, the main heroine (the titular yellow dragon, an uber powerful being) is BrainwashedAndCrazy. Her friends decide to rescue her from a group of kidnappers (who are technologicaly advanced kingdom that want to use her as a weapon), no matter what it takes. We see a castle she was held in exploding, and we then learn that she never got under their control. She was just playing along to see what her friends will do, but didn't want to wait any longer, so she freed herself. Offscreen.
In Majokko Tsukune Chan, there's an episode called "Tsukune-chan vs. Aliens." It's five seconds long, and all we see is the Mayor asking Tsukune-chan for help, and then a brief shot of the alien ship blowing up. Afterwards, an off-screen voice says "But I wanted to see that..."
In Saiyuki, Hakkai takes of his demon power limiters to take down these highly annoying immortal demons, we lean forward, they go back to the other characters, we're like "okay, they'll go back to it in a minute" and the next time you see him is going to help Gojyo. The fight was skipped. Completely.
In one episode of the anime series, Kenshiro fights an army of Ken-Oh's ninjas armed with poisonous weapons. Before Kenshiro kills any of them, it cuts to Raoh storming the Nanto capital. Shortly after Raoh destroys the gates and slaughters hundreds of guards, it cuts back to a pile of dead ninjas, just in time for Kenshiro to resist the poison and kill the ninja leader.
Black Cat is very strange with this trope, and way too fond of it. They'll have occasions where they show just the beginning and end of fights, beginning and middle of fights, the middle of interrupted fights, and the beginning, middle, and end of a fight but without actually showing how the victor won. Basically, whenever opposing groups of badasses congregate in one place, you're not going to get to see much of the action. And since the badassness performed on-screen is damned near off the charts, it really makes you feel like you missed something. It reaches its peak in the Train vs Creed fight, where after a long and brutal battle Train fires his ultimate attack, misses, and somehow wins anyway. No explanation is given except for a flashback of the ultimate attack sailing past Creed. And still completely missing. Maybe more of an Unexplained Moment of Awesome, but it is still disappointing.
That last example is only in the anime. The manga's a bit better about this trope.
Trigun anime Episode 18: Vash and Wolfwood are about to take on about two hundred men to save Lina. We are then shown Vash getting his hair cut by Lina post-fight, as well as the ruins of the battle.
In the corresponding Trigun Maximum chapter (the very first one), the large fight is also skipped, but Vash confronts the imposter holding Lina against her will and defeats him.
Subverted in the first episode, where Vash gets up and without fear points his gun at the criminals and one hears a gun going off. It isn't until sometime later during said episode that it is revealed that Vash forgot to put bullets in his gun and ran off while getting shot at.
In Fairy Tail during the Phantom Lord Arc Mystogan visits Porlyusica and reveals that he defeated every subdivision of Phantom Lord by himself and proves this by scattering all the subdivisions' flags across her yard. He also reports that he was the one responsible for regathering Makarov's magic power, which was drained from his body by Aria, giving him the strength to defeat Jose Porla.
Erza destroys 100 monsters of the Pandemonium this way. It is expanded in the anime.
In Saiyuki, Cho Hakkai's youkai form isn't shown to the audience until well into the series. Consequently, his first two battles in that form—one where he took out a basement full of gangsters and one where he killed a huge monster—take place entirely off-screen. Given that the monster fight freaked out even the combat-loving Goku, this probably overlaps with Gory Discretion Shot.