GunBuster: The very first occurrence of this trope, originally designed to add more realistic movement to running and walking, but it got out of hand in later years. Even so, it got the show a Fan Nickname of "Bust Gunner".
In Akane-iro ni Somaru Saka's eighth episode, whenever the camera focuses on Tsukasa, her breasts appear to take on a life of their own. The first scene, which is just a profile shot of her laughing, has them bouncing up and down like crazy.
Yurika in Akikan! actually uses Gainaxing as a strategy. In a baseball game with Yell (who's distracted by moving objects), she apparently plays without a bra on purpose, leading to very springy bouncing that Yell just can't take her eyes off of.
The title character in Amazing Nurse Nanako falls prey to this, making an otherwise well plotted series difficult to watch.
Exaggerated to the point of ridiculousness in The Ambition of Oda Nobuna, where Katsuie's boobs manage to jiggle in full Breast Plate. Yes, apparently her boobs are so ridiculously bouncy they can bend metal.
Miyuki in Basquash!, who has her bouncing breasts take up the entire screen for a good few seconds. Which is taken to the next level with Haruka Gracia, who we get to see jiggle on three separate occasions before actually seeing her face.
Played for Fan Disservice in Berserk with Casca, as the only time we see this happen is during her rape by Femto, where the gainaxing actually serves to show how violently she's being assaulted.
In chapter 117 of Black Cat, one panel has Saya Minatsuki dodging Creed's slashes, causing her breasts to swing in visibly different directions. She's far from the bounciest female in the series, but she does seem like the kind of girl that would go without a bra in the comfort of her own home (which is where she was when that asshole Creed barged in on her).
Played for Laughs in the animated omake of Black Lagoon, when Rock wakes up as a woman... "WITH HUGE BOOBS!". In the series proper, Revy's very acrobatic Gun Fu causes this to occur during her fight scenes. More noticeable in some than others. At least in her case it's justified as it's canon she doesn't wear a bra.
Just about any female character in the various Burn Up! animes. ADV's release of Burn Up Excess featured a toggleable alternate subtitle track that actually displayed a tally of how many boob-bounces are shown on screen of each character's chest!
Rosette does this in the third episode of Chrono Crusade — unfortunately bad animation makes it look as if she had bags filled with water instead of breasts.
Kyou Fujibayashi of CLANNAD Gainaxes like mad in the opening credits of the first season, while bouncing a basketball. Kotomi also does so in the Baseball Episode.
This happens to Milly and Shirley during one of the School Festival activity episodes in Code Geass and to Kallen, the most noticeable example being her encounter with Suzaku on Kamine Island. You'd think that Kallen, having one of the larger chests of the female characters featured on the show as well as being the most physical girl, would get a lot more of this during the action sequences but the total count reaches no more than a handful. Well, any more than a handful is a waste.
Cowboy Bebop has the character Faye Valentine, who is breathtakingly beautiful with gigantic pneumatic breasts that seem to have minds of their own. Canon indicates that she does this on purpose to distract men. On one occasion, she wears a perfectly normal evening gown.
Junko Asagiri from Desert Punk has numerous instances where her huge breasts move out of sync with the rest of her body. In some cases, usually when she's trying to seduce someone, her breasts bounce on their own.
A certain animation team in the rotation for Digimon Savers used this technique on Rosemon, and it's probably not a coincidence that they animated BioLotusmon's only appearance. It's worth noting that before Savers, the only minor use of this trope was in the second Tamers movie — Sakuyamon's bounce a bit when she's freed from a Parasimon tentacle.
Digimon Xros Wars has Lilithmon and her boobs (she even fondles with them), and then there's Mervamon for the good guys (the opening even has her boobs bounce!), who even fires lasers from her breasts.
Practically every female role in Divergence Eve and its follow-up. It may be noted that outside of this and the fanservicey opener and closer, the series is remarkably serious in tone and tells its story in blissful.
Happens to Caulifla in episode 114 of Dragon Ball Super when she does a boxing stance during her fight with Goku.
Siesta pictured here◊. You're probably not looking at the Love Bubbles surrounding her. Used to great hilarity in one episode when the gang is trapped in a cave. They hear something approaching fast and prepare for a fight, until Saito realizes exactly what that sound is with a priceless look on his face while the viewers get the obligatory chest shot of the approaching Siesta (who's wearing the Sailor Fuku outfit Saito bought earlier).
Not to mention Kirche the Ardent. Until Tiffania's debut she was the most buxom character in the series and do often this in the first season.
Siesta is nothing compared to Tiffania, who barely has to move to set her breasts bouncing around like Flubber and is often subject of Gag Boobs. In the closing theme for the third season, they shift like a waterbed while she's standing still.
Haruhara Haruko in FLCL. It is Gainax after all. Of particular note is the random bunny suit she wears during the big battle in episode 5.
Ikumi Mito in the anime of Food Wars!, especially in her usual bikini-top getup. Just sticking her arm out and leaning over slightly is enough to send her breast into a frenzy!
This happens in episode 19 of Fullmetal Alchemist: Brotherhood; for unexplainable reasons beyond pointing out that Havoc likes big boobs, Lust's boobs bounce considerably.
Angela, an American visitor to Genshiken, displays this conspicuously (complete with bouncing sound effects) to make the differences between Japan and America (or at least Eagleland) more obvious, and to highlight her more upfront attitudes about sex (she is an unashamed Yaoi Fangirl) and maybe a bisexual (she was at least interested in the male oriented hentai as well). Oono also gets this quite often.
Almost every female character in the anime Girls Bravo. First seen with Miharu while she and Yukinari are running away from the mob of women on her home world, Seiren, during the first episode. The opening scene of the 13th episode shows Kosame shadowboxing while in the shower; during which her breasts bounce with each of her strikes.
Godannar takes Gainaxing to the extreme, since even the mecha have breasts (and in one particular case, both the mecha and the pilot have humongous jiggling breasts). The only exception to this is Lou, the show's Token Mini-Moe.
Golden Boy did this quite a bit, especially in the first episode (from the owner of a computer software company).
Plentiful in Gravion (which provides the image in the trope's main page), especially with Mizuki Tachibana, who bounces considerably with the slightest movement, even swallowing. Gainaxing is a signature of Gravion's creator, Masami Obari, present in his works, including the Fatal Fury anime adaptions and Voltage Fighter Gowcaizer, in which it's put to the utmost extreme.
While not exactly as flagrant, Murrue Ramius of Gundam SEED has the dubious honor of having her bouncing chest be one of the few whose bouncing was actually animated and used as Stock Footage every time the Archangel took a particularly nasty hit in battle. On top of her introductory shot being to turn around in surprise when the Archangel is bombed upon docking, wherein her breasts bounce and take up the majority of the frame. This seemed to be limited to her, until first officer Natarle Badguirel ended up in command of her own ship, whereupon she gained the suddenly bouncing breasts (albeit not as dramatically given her modest proportions), as did Flay Alster as part of her crew. Whether this is actually an accurate depiction of how breasts move in zero gravity is debatable.
Murrue was also the first woman in the Gundam franchise to have her jiggle in the opening credits of the actual series itself. She was replaced in the HD Remaster by Fllay Alster. The James Bond opening credits level nudity is also bra-less and even had male viewers often going "...those don't work that way." Female tropers, on the other hand, winced in pain and often skipped those credits.
"They wounded the burst-proof battleship in order to sway the heart of the captain." - Moetan II, volume 1 (the book). Obviously, the word "heart" in the Japanese translation can also mean "breasts".
Parodied and lampshaded in an anime-original RPG Episode of Hayate the Combat Butler where the bouncing boobs of the RPG game's boss is focused on constantly and has a sound so audible a character points out that she hears the sound of the bouncing from a considerable distance away.
Mii in Jungle de Ikou! Gainaxes quite a bit, thanks in part to her huge rack (Mii's breasts are supposed to represent Earth's life-giving energy); this is taken to a somewhat absurd level when Mii uses her powers to turn into a giant.
Kill la Kill has this with Ryuko and Satsuki, especially during their transformation sequences..
In Kirby: Right Back at Ya! the appropriately-named Bouncy Tiff, who is created to the real Tiff's dismay. She is drawn like a stereotypical magical girl and... err, deserves the "bouncy" portion of her name. Even the youngest character in the crew knows to cover his eyes.
Happens at one time or another to most of the female cast of the anime releases of the KoihimeMusou franchise who have large breasts, especially to Kannu. Ryuubi even gets to do it on purpose later in the series to lure someone into a trap.
Yuriko deliberately does this to Daichi while on the train in episode 6 of Kotoura-san. He ignores it, much to her frustration.
Ladies Versus Butlers! is full of this, having ample fanservice moments. Sernia Iori Flameheart in particular, she even gets the sound effects, generally the other girls don't.
Chapter 95 of the manga Mx0 plays this trope for satire with a magical liquid that makes some (already extremely buxom) girls' breasts experience only 1/6 normal gravity. The result is a lot of bouncing, first from falling, then from wind, then an earthquake.
Macross Frontier features a whole raft of characters with sufficiently Gainaxed breasts, including Sheryl and the Miss Macross Frontier contestants (which makes Ranka uncomfortable.) Also, zero gravity bouncing. Very unique. When a fully sized, thirty-foot-tall Zentraedi, Klan Klein has a rather terrifying bust that may actually be capable of killing a normal-sized human. Micronized, however, she doesn't possess anything that can be Gainaxed.
Also very evident in the ending credits, especially at 13 seconds - 16 seconds (she's on the right). It's even lampshaded in a Season 2 dub outtake - "Look at these things, they move independently of each other!"
Quetzalcoatl/Lucoa from Miss Kobayashi's Dragon Maid has the largest boobs in the group and is the most prone to gainaxing. Tohru and Elma's introduction scenes also have their undeniably large breasts bouncing, what with Tohru's doing it upon landing in front of Kobayashi, and Elma's as she was standing up after her dynamic entry into Kobayashi's home. It seems that all dragons end up growing huge tracts of land when they come of age (Kanna doesn't count, since she's a child by dragon standards).
Miss Machiko was perhaps the first anime to do this, although the gainaxing in that show is tame by today's standards.
Centorea in Monster Musume. Her breasts bounce a lot thanks to their size and her lack of a bra. This actually turns out to be a problem in Chapter 29, as the bouncing keeps throwing off her aim while jousting.
Chu's entire entourage in Mouse, even the flat chested one.
Mai from My-HiME dresses conservatively, but her somewhat large (but not Gag Boobs-level) chest still has a bit of bounce to it. A scene early in the anime replicated during an argument with Yuuichi and Shiho gives them an audible "boing". According to supplemental materials, it's not even Mai who has the largest bustline. She's beaten out ever-so-slightly by Haruka, who doesn't have a whole lot of bounce, but still looks good in a swimsuit.
Strangely enough, while attention is frequently called to her lack of a chest in the original series, Arika in My-Otome Zwei starts bouncing quite noticeably, especially whenever she prepares to use her signature move. One could argue, though, that she has filled out in the one year since the end of the series.
Mai Kawakami in the animated adaptation of Myriad Colors Phantom World is probably the bustiest girl on the show, and jiggles quite a bit. In the first episode Mai is the last contestant in a limbo contest. Unfortunately, she's also in danger of losing because her large breasts won't fit under the rope. To get under the rope she starts bouncing her breasts so that when they reach their lowest point she slips under the rope. Note that this would really only work in real life if 1) she wasn't wearing a bra and 2) her breasts were made of jello.
The seventh movie had the girls bounce from doing absolutely anything. Hell, in a few scenes, Nami will simply be standing around, perfectly still, and her boobs will just randomly bounce quite forcefully all on their own.
And in the twelfth movie ''Z'', where Nami's breasts jiggle often for little reason. Although one could argue this is compensating for the fact she spends most of the movie turned into a child.
Done poorly with Bekira in Our Home's Fox Deity. Kind of lampshaded by Noboru taking a quick glance at Kou's assets for comparison. Subverted later on when it turns out those weren't actually her breasts.
The sheer quantity of gainaxing found in the anime Plastic Little inspired ADV, the North American distributor/dub house, to include an on-screen "Jiggle Count" meter as one of the special features in their DVD release.
Queen's Blade episode nine introduces Cattleya, the franchises bustiest character with a 120cm bust size. Despite the size her of her breasts, which would be very heavy, in that specific episode they are given extremely floaty animation. In one battle, blocking an attack manages to bounce them so high they cover her face.
Rail Wars!. From both the main girl, but Haruka is the most focused on. For example, during the track scene in school, the camera goes to Shou, confirming his athletic ability, whereas the camera goes to Haruka panting and her breasts bouncing everywhere.
Every female character that appears in the various Ranma ½ motion pictures — even the ones who are supposed to be small-breasted. This contrasts with the main series where they never seem to move at all, since the show is kind of old and didn't have a huge budget. May be at least partly Creator Appeal, on the part of animation director Atsuko Nakajima, who was so infamous for drawing her characters this way in the mid-90s that it earned her the nickname "Knockerjima".
Studio Gainax is responsible for animating the Re: Cutie HoneyOVAs. Hoo boy, is there ever Gainaxing in that show.
R.O.D. TV had one particularly infamous chase sequence where Nenene finally finds her long lost friend (love?) Yomiko Readman. Yomiko runs away and Nenene gives chase. As they sprint, their bosoms (which had been largely still until then) bounce and sway like jello earthquakes. It's also worth noting that Yomiko's bustline went from a mild C-Cup in the OVA well into DD territory for the TV series, set several years later. A late blooming?
It isn't just the chase scene. Watch Nenene's bosom in the first episode. They ripple like water.
Kurono Kurumu in Rosario + Vampire. The movement of her breasts even produces audible sounds! And in episode 4, Kurumu's fat stalker (or rather, his belly).
Surprisingly, several girls in the Saiyuki anime jiggle around in action, even though the show is mostly fangirl fodder. Then again, the franchise was originally marketed as Shonen.
Nodoka of Saki says hi. Just the simple act of walking could get her breasts jiggling. A critic from the Anime News Network site once noticed that her entire wardrobe is sewn in just the right way for her shirts to perfectly cup her chest.
Sakura Trick does that on Haruka's self-declared D-cups. Kotone sometimes has this treatment.
Parodied in Samurai Champloo when small-chested Fuu decides to carry a couple of cherry bombs by sticking them down the front of her kimono. And then she goes for a run. The result is quite comical, which is compounded by the occasional viewer who didn't notice the cherry bomb thing and thinks that her breasts have just gone insane.
The SHUFFLE! OVA had Sia and Asa Gainax within the first three minutes. Then when Sia's dad replaces the water in the pool with eels, Nerine does as well.
Happens a few times in Slayers, with the leading contender being the balloon-breasted Naga the Serpent; it almost got her killed once, her rack sprang back into shape after being pressed against a wall, nearly launching her over a cliff. Surprisingly, Amelia, one of the protagonists, is quite busty (to the point that Lina hates her for it), but she isn't subjected to this trope, save for the Slayers Premium movie, where it's actually used as a part of her flanderizedchew toy status. Newer anime seasons also made up for this by having Amelia be subjected to breast-squeezing Combat Tentacles in one battle, and then having her tunic partially ripped from her breasts after another battle.
Yoko, and Kittan's three sisters (who come in small, medium and large for your viewing pleasure) in Tengen Toppa Gurren Lagann. Guess who it's made by. In fact, the English trailer for Gurren Lagann contained the words "that famous Gainax bounce". Yoko is an especially amusing example because her breasts seem to spontaneously Gainax without any movement on her part, whenever any attention is called to them.
Done hilariously in the Beach Episode of Tokimeki Memorial Only Love with swimming team captain Koayu Utsumi, whose Gag Boobs jiggle just from her merely looking around, complete with sound effects (and it doesn't help that it's getting all the attention of all the guys around, which she hates so much, and especially since she's on lifeguard duty at the time).
To Love Ru seems overly fond of this. Espically Lala. Just watch the OVA opening, 1 minute and 30 seconds of pure bounce.
Even one of the more serene shows, Umi Monogatari, gets a chance to indulge in this trope. Oshima, Kanon's rival, is flaunting her own bust size, when Marin comes running up to greet her. Marin, already halfway to being an Innocent Fanservice Girl, is not wearing a bra. The results leave Oshima stunned.
The anime of Umineko: When They Cry gave most of the women and girls a bad tendency to do this, which would be fine if this were a comedy series. Unfortunately, Umineko isnotacomedy series. Poor Shannon has the worst of it. Every time she makes a sudden movement or reacts to something, her boobs also react, with a single bounce.
Valkyrie Drive: Mermaid has a lot of it. Let's just say if you have anything approaching a decent cup size, you're going to be bouncing all over the place.
Why the Hell Are You Here, Teacher!?: Ouka has this problem whenever she runs. We see this when Yamato is tasked with teaching her alter ego Sakura how to properly run on a treadmill, and again in a flashback which shows her annoyance at the boys who notice her when jogging.