One short story in Binbougami Ga has Momiji forcibly switch bodies with Ichiko, in order to ruin her reputation. Before leaving Momiji brags about how awesome it is to have big breasts only to come back about a minute later to complain how burdensome large breasts are and tell Ichiko she feels sorry for her. Still doesn't stop her from wanting big breasts, however.
Yae from Hanjuku Joshi really hates having large breasts, even wearing a painfully small bra in an attempt to flatten them down.
Miu Fuurinji in Kenichi: The Mightiest Disciple laments her size, mostly due to how it interferes with her being a martial artist. The fact that several characters call her a dairy cow contributes to this.
Natsumi Hinata from Keroro Gunsou is reminded more often that she'd like that (usually by the Schoolgirl Lesbians stalking her) she's more well-endowed than average, and seems to think they're more a burden than a blessing. One of her fears is that she'll "end up a mutant like mom" and the effects of Kururu's age-changing beam in volume three indicate that this is indeed destined to be her terrible fate.
Yuna from Mahou Sensei Negima! is annoyed about her bust growing since it gets in the way of playing basketball.
Oiso from Manyu Hikencho is notable for being one of the few large breasted women in the series to hate her breasts. She was formerly her village's best diver but her breasts grow so large that they got in the way of her diving. When Chifusa ends up having to use the breast-absorbing technique on her, shrinking Oiso's breasts, Oiso is grateful.
Roxy Simpson from Planetes has "a complex about her breasts" as Tanabe puts it. Planetes being a highly realistic and mature series, this is one of those rare examples where this trope is played rather seriously. Roxy works as a receptionist and the way men keep harassing her and asking her on dates makes her worried that she looks slutty.
The fact that she used to be a prostitute doesn't help.
Shii of Puni Puni Poemi has an absolutely enormous chest, large enough that she has to set them down on things around the house to keep from falling over, including the title character's head and apparently once smothered the cat. When each of the family members gets an Imagine Spot for what they'd wish for with Puni Puni Poemi's magical powers, Shii's spot shows a flat-chested version of herself.
A more downplayed version appeared in Servant × Service, where Yamagami actually relieved that Chihaya guessed her chest puppies' size to be merely F-Cup!
Yuka Takeuichi from Variable Geo gets depressed over that the fact that her already large breasts are still growing. It's mainly because it's cause her work clothes not to fit properly.
In Hagure Yūsha no Estetica, Myuu does not like her huge rack because it is difficult to find clothes that fit her, and she keeps popping buttons.
Miss Aoshika from Wolf Guy - Wolfen Crest has had large breasts since the time she was a teenager, and they've attracted her a lot of unwanted attention (and what's more people tend to claim that she's "asking for it" due to her figure).
Motoko Aoyama of Love Hina gripes at one point that, since her breasts are so big already and still growing, it makes it harder for her to wrap her sarashi.
Furutani Himawari of Yuru-Yuri is notably stacked for a 13-year old and does not enjoy it as she feels it alienates her from her classmates and brings unwanted attention. Not to mention it drives her best friend Sakurakonuts
This is a part of Sakaki's poor self-image in Azumanga Daioh, along with being a Huge Schoolgirl in general. She's not got Gag Boobs by any means, but she's rather buxom compared to the Japanese stereotype, and noticeably more busty than any of her friends.
The idea is briefly toyed with in Yet Again with Tsunade, with the narration casually mentioning that what keeps them from being an inconvenience to her is a basic chakra control exercise.
Cordelia in Blue Belle is highly irritated that one of the leftovers from Halloween is an additional two cup sizes, mostly because it's hard to find bras in an F-cup.
Mentioned in Superbad by the two protagonists (sex-obsessed teenage boys) when discussing a woman's breast reduction surgery. One of them points out the back problems they caused her, while the other one claims that opting for this surgery is akin to spitting in God's face.
In the short film Size 'Em Up, a teenage soccer player is dragged to a bra shop by her mother. She's already reluctant and uncomfortable, and becomes considerably more so when the clerk checks her out and declares that she's a 34DD, because she had never even heard of a size like that before.
In American Psycho, Patrick Bateman is a fan of a fictional talk show called The Patty Winters Show. One morning, one of the guests on the show is a woman who once had large breasts but underwent breast reduction surgery. Naturally, Bateman and all of his colleagues privately ridicule her for her decision.
In Are You There God? It's Me, Margaret., Margaret and the other girls envy Laura Danker, who developed breasts early. Boys ogle her and girls circulate gossip about her. Later in the story, it's revealed that Laura wishes she didn't have them: she doesn't like the attention they attract.
In the Dragonlance novels, Tika Waylan feels awkward and dumpy because of her big breasts and is envious of the elven princess Laurana's slender figure.
In Cauldron of Ghosts, Yana is aggravated that her disguise includes large hips and bust, due to them throwing off her balance and being a general inconvenience to an Action Girl.
Morgan from the Once a Thief series has a very generous bust, and has always hated the attention it attracts. Before the beginning of the story, she would wear multiple layers and unflattering clothes to downplay the size of her breasts. It's commented on quite a few times in the series, and it embarrasses her every time.
In Dr. Quinn, Medicine Woman (episode 3x12, "Ladies Night, Part 2"), Colleen tries to bind her breasts and tells Dr. Quinn, "I don't want them" after receiving inappropriate attention from the boys in town.
One episode of Malcolm in the Middle had Malcolm's friend with this problem, always wearing overly-large sweaters to hide her chest. When Reese finds out and tries to seduce her just for the chance to see them, Malcolm has to try to stop him without letting Cynthia know he revealed her secret.
In an SCTV parody of "The Nutty Professor" with Ed Grimley, the love of his life is despairing over their supervisor's boorish harrassment:
Stella: Oh, why was I born with these big bazongas?
Ed: Oh, I'm sure you weren't born with them; I'm sure they developed over time, ya know?
On Two and a Half Men, Chelsea (to whom Charlie was engaged for awhile) contemplates breast reduction surgery to help with back problems she'd been having (on the advice of Alan, who's a chiropractor). Charlie desperately tries to talk her out of it.
An episode of Roseanne had her doctor suggesting a breast reduction because of the back pain she had been suffering. Before the operation, she has a nightmare that they gave her a breast enlargement instead.
In The War At Home, teen Hilary is suffering A-Cup Angst, wishing that she had larger breasts like her mother. Mom says that having big breasts is a pain in the back, literally.
On My So-Called Life, a list made by the boys at school circulates that rates various girls. Sharon is mentioned for her large breasts, which makes her very self-conscious. (Angela, on the other hand, isn't mentioned at all. Angela's mom insists it's better to blend in then it is to stand out, but ultimately the Aesop is that the list dehumanizes all the girls whether they're "praised," insulted, or left out entirely.)
A hilarious monologue in the mostly serious play How I Learned To Drive has the main character comparing her emerging boobs to parasitic aliens who have latched on to her.
Litchi Faye-Ling from BlazBlue downplays this a bit. She isn't entirely ashamed of her figure, so it isn't H-Cup Hell (seriously), but the big part of her cosplay fetish (seen in the various gag reels) is that she can't wear the outfits herself due to her figure.
Sypha from Castlevania Judgment is pissed off that she has such large breasts. This is only mentioned in Maria Renard's story, where Sypha is one of the three characters that Maria has dialogue in outside of the pre-match words.
Misfile Ash hates having large breasts (that are still growing) and would rather be a flat-chested girl everyone ignores. This is because Ash used to be a guy and would really much like to be one again.
Chanel of Rain is one of the shortest students in her school and she has big breasts, which attracts a lot of boys...except she's afraid of boys. And she's homoromantic. Chanel has some resentment toward her breasts.
Natani of TwoKinds is similar to Ash above; because of a near-fatal Black Magic spell in her youth, part of her soul was torn away and had to be replaced with a transplant from her brother. This means she is fundamentally a transsexual, identifying herself as male despite her female form, and so her breasts are just a reminder that her body and mind don't match. Normally she's indifferent - the breasts are easily held back by a good set of bandages and a thick jacket - but she finds plenty to complain about in the regular heat cycle she experiences.
Played with in The Simpsons episode "Large Marge", where, due to a screw-up by the hospital, Marge ends up with breast implants. Initially, she wanted to get rid of the implant as soon as possible, hiding them from her family, but she soon enjoys the extra attention they bring her. Later, however, the attention becomes too much, she starts getting backaches, and by the end of the episode she has the implants removed.
Soleil Moon Frye, originally known as a child actress in Punky Brewster, became so endowed when she matured that she elected to have breast reduction surgery before she was 16.
Something similar happened to Argentinian actress Florencia Peņa.
Many times, female athletes, especially in sports where people are expected to move around a lot, prefer a "lean, mean" look since a large bust can actually be a handicap. This is one aspect behind the design of athletic and sports bras: helping to contain them and reduce their movement. There are also exercise regimens meant to help tone the bust, resulting in tighter and firmer breasts that don't move so much. In extreme cases, some women opt to undergo surgery to reduce cumbersome breasts down to a more manageable size.
One example of the latter is Romanian tennis player Simona Halep. Her large breasts interfered with her game and were sometimes physically painful during play, so she had them reduced. (Though she said she would have done so even if she had not been an athlete).