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In one currently airing reality show commercial, a preteen boy and his older sister go in for a chest bump. However, the older sister is definitely outside of his age range and looks suitably more mature. So they go up for the chest bump normally, but he winds up on the floor.
In The Ladders advert at the beginning a man is pushed over by a woman chest first 
Konohamaru does the same thing, but he likes it — that is, before he realizes who it is.
Natsuki's half-trip/half-push-into the amazing Haruka in Minami-ke. She knows it's an accident, but punches him anyway to make it clear to everyone that it's Not What It Looks Like. Still worth it. And he agrees with the punch.
It's happened many times since then, but in a one-off special, Bleach's Toshiro Hitsugaya's very first meeting with his future lieutenant Rangiku Matsumoto is when she rams into him, chest-first. It's Meet Cutewith two zeppelins. He's knocked off his feet; extraordinary.
Ogiue's run-in(to) with Ohno at the Comic Fest in Genshiken.
A gentler one: in Mahou Sensei Negima!!, Negi's first meeting with Shizuna-sensei. It's used as a straight Marshmallow Hell to establish that he's still a child, when he's merely embarrassed. Although in this case, it's more of a "wumph" than a "boing."
From the above scene: "Can I... have a cookie?"
Ironically, the Marshmallow Hell incident that gave that trope its name was actually started by a Funbag Airbag moment: Negi didn't watch where he was going while swimming, smacked headfirst into the bustiest girl in the class, and somehow got caught in her bikini top in the process. The other girls just took it way too far (as usual for them).
Actually she blushes, yelps, bolts a short distance down the hall, then turns and yells "Idiot! Pervert! Sicko!" back at him. She does hit him later on in the episode, but that was right after she snapped out of the blank state that witnessing a highly destructive supernatural confrontation had put her into and started having a massive freak out, so it may not have had anything to do with the earlier incident.
In the following episode, once they reach the school, Shiho questions Yuuichi about their meeting while the Funbag Airbag scene replays three times in the background.
Variation: Vandread has Hibiki falling into the...other cleavage.
Comic Party has this same thing happen to the male lead in the fourth episode. He takes several seconds, during which the female even cheerfully asks if he's alright, before he finally realizes what's occurred.
Simon is walking with his head down and ashamed of being a driller... when he bumps into Kamina's waist. The only thing that comes out, though, is Kamina saying in an encouraging tone "Walk with your head tall and proud, Simon!".
A more traditional version happens with Simon landing on top of/in between Yoko shortly after they first meet. She gives a heartwarmingly reassuring smile when they make eye contact, showing that she understand it was an accident and isn't mad at him for it.
In Martian Successor Nadesico: The Prince Of Darkness, Harry first meets Minato chest-first. The poor boy ends up with a full-body Luminescent Blush before he can disengage. The dub takes it a step further, where deep in his self-recrimination (the reason he was so distracted), he calls himself a boob just before impact.
Baccano!: Jacuzzi Splot gets one of these when he runs into Isaac and Miria in a cramped hallway aboard the Flying Pussyfoot. For extra points, Jacuzzi accidentally catches on Miria's (strapless) dress and pulls it down as he falls, meaning he doesn't just get a face full of Miria's boobage, he gets a face full of Miria's naked boobage. Poor, lucky bastard.
It's never acknowledged by the characters, but in the first episode of InuYasha, when Mistress Centipede has Kagome pinned to the sacred tree (and thus, Inu-Yasha), Kagome's face is pretty much right in Inu-Yasha's crotch.
Zatch Bell!. In episode six, Kiyo has his book stolen by a disgruntled patient and attempts to chase after the patient. However, he ends up running straight into the chest of a nurse who proceeds to JAM his head in there so as to keep him from running away, seeing as he's still recovering from an attack. From then on it becomes a Marshmallow Hell.
In the first episode of Maburaho, Kazuki accidentally runs straight into Kuriko's chest. She then places him in Marshmallow Hell.
The fourth Black Lagoonomake has Rock colliding with Chang this way. It mainly served to reinforce the Gender Flip of the cast he was panicking about.
In Infinite Stratos, this happens when Lingyin was running away from Cecilia. During which, she runs face first into Chifuyu's breast.
Inverted in Rosario + Vampire: When Kurumu dives into Moka's mind to rescue Tsukune, Mizore, and Tohofuhai, the first thing they see of her is Kumuru flying in, wings and tail ready and everyone is wondering how the hell she got in there. Then she glomps Tsukune at flight speed. You'd think that would hurt, but when she's upright again, Tsukune is just buried in her cleavage. No harm done.
Inverted in "Sekirei": Minato's first encounter with Musubi happens when she literally falls out of the sky onto him, boobs-first to the face.
Happens in the first chapter of Koko Ga Uwasa No El Palacio.
Happened in the first episode of Maicchingu Machiko Sensei when two boys steal the eponymous character's panties and try to run away, only for her to head them off around a corner.
In the nineteenth episode of Yu Gi Oh ZEXAL, Yuma, in his rush downstairs to get to class, doesn't notice his older sister Akari, until he crashes face first into her breasts, getting knocked flat on his rear from the recoil.
In After War Gundam X, Garrod accidentally does this to Pala Sys, twice in the same episode.
Little Busters!: In one scene, Kud is running to catch a ball and accidentally runs into Kurugaya's hefty chest. Though Kurugaya's immediate response is to hold her head in place, regardless of Kud's flailing or the sweatdrops of the other girls around.
Happened once in Strangers in Paradise. ("I'll give you first base, but second will cost you your legs.")
In Penthouse ComiX, this is how Young Captain Adventure meets Hericane. He's embarrassed but she's fascinated by him. This leads to Slap-Slap-Kiss and Destructo-Nookie on a superhero scale a few pages later.
Happens in Kitsune no Ken: Fist of the Fox, during one scene when Naruto is fleeing from Ino and Choji (who both want to beat him up for spilling a pudding and a burger)...and winds up running right into Kurenai's chest. Kurenai takes it in stride at first, but later gets comically unhinged when Kakashi teases her about it.
In Discworld fic The Lancre Caper, a young stealth archaeologist called Alice Band is outclassed by a peril she has never before encountered - Nac Mac Feegle. Whilst holding her immobile, one imprudent Feegle discovers human women have breasts. And goes bouncy-castle until restrained by the Big Yin.
Films — Animation
Happened chastely in The Iron Giant for a quarter of a second. Special Agent Kent Mansly (He works for the govern— SLAM!) knocks on the front door of the house, rehearsing his lines and staring at Hogarth's damaged BB gun when the door is opened by Hogarth's mom, Anne. Kent rapidly raises his head to talk to her and smacks it accidentally into the underside of her ample cleavage, resulting in a BOINNNG sound.
In the live movie adaptation of How the Grinch Stole Christmas!, the eponymous character ends up being ejected from a garbage chute, ricocheting off a drum, pulling a banner like a slingshot, and landing with his face in the cleavage of Martha Mae Whovie. "Hello, Martha."
On my way up the stairs, though, I walked straight into the medium herself, surrounded by her entourage. I bumped right into her, my nose centimetres away from her plump pink bust.
Star Trek: Enterprise. Captain Archer and his Ms. Fanservice science officer T'Pol are captured and tied together by rebels in "Shadows of P'Jem". Whilst struggling to free themselves they trip and Archer's face ends up right between the best Vulcan peaks outside Mt. Seleya.
Two and a Half Men: Alan and Charlie are removing a passed out, scantily-clad woman from Charlie's bed, and Alan, who is carrying her by the arms, slips and falls on her. We don't see how he falls, but we do hear his muffled reply: "Oh, my God! They're real."
That would be the lovely Diora Baird, who's made most of her career off having Gag Boobs.
This happens to Jin and Asuka during Asuka's ending in Tekken 5 Dark Resurrection. Jin is disoriented after reverting from his Devil form to his normal form, stumbles, and lands face-first in Asuka's cleavage. She shoves him away after about ten seconds, leaving him disoriented and confused.
A more literal example in the flash-game Nanaca?Crash!!, where running into Misato (the girl in green) usually ends the game immediately.
Humorously subverted in the Metal Gear Solid 3 short "Metal Gear Raiden: Snake Eraser". Raiden time-travels to the scene of The Boss showing Naked Snake a scar on her chest, and so happens to teleport in such that he's making a beeline for her cleavage. He stares at it for several seconds, then gets bitch-slapped by her, Snake gasps in horror, and Raiden teleports out once more, but not without the Colonel shouting "TIME PARADOX!"
In the pilot of Korgoth of Barbaria, one of the thugs in the bar fight gets flung across the room by Korgoth, and he lands face-first in a barmaid's cleavage. He doesn't leave to rejoin the fight (considering the guy he was fighting, it's an excellent idea).
In Family Guy, Quagmire makes this trope literal. His car has blow-up sex dolls in place of airbags, so when he crashes it results in this trope.
Happens to Woody Woodpecker in the cartoon "A Fine Feathered Frenzy." While he is trying to escape from Gorgeous Gal, a love-struck old overweight yet wealthy crow he opens a door while not looking where he was going. Behind the door Gorgeous was waiting for Woody with her lips puckered. He runs right into her chest and bounces off. Since she was so overweight it's not apparent that his head lands into her breasts right away. Before he bounces away she grabs him around his waist, gazes at him lovingly and kisses him on both cheeks. The Woodpecker escapes even though there's a lot more propositioning, flirting and kissing from Gorgeous Gal in his immediate future.
Gravity Falls: In the second season episode "Into The Bunker", when Dipper and Wendy are inside a decontamination chamber, air vents push them together. His face lands on her chest, but they bounce apart so quickly that Wendy doesn't seem to notice and Dipper only looks very briefly. In the original storyboard,◊ they're left that way until both realize what happened and separate themselves in a panic.
Regular Show: In Starla's debut episode "Muscle Woman", Rigby accidentally walks into her chest when they go to confront her.
Truth in Television
In a rather literal twist on the trope name, a woman with implants was saved from serious injury in a car crash by her augmented breasts, which served as airbags.
Same goes for all-natural Playboy playmate Petra Verkaik, whose breasts literally saved her life when she was working underneath her Volkswagen Bus when the jack collapsed. During her recovery her doctor told her that if she hadn't been so well-endowed she probably would have sustained fatal chest injuries.
According to her autobiography, this happened to former WWE Diva Chyna when she went to the Emmy awards. Joan and Melissa Rivers wanted to interview Sarah Jessica Parker; her husband, Matthew Broderick, politely stepped back out of the way, didn't look where he was going, and accidentally parked his head right between Chyna's boobs. Since Broderick is 5'8" and Chyna is 5'10" and was likely wearing heels, it's plausible.