In contemporary Japanese settings, kimono is often shorthand for "this character appreciated the traditional Good Old Ways". Even people who wouldn't normally even think of abandoning the comfort of Western wear, will go out of their way to wear fancy kimono for formal celebrations and events. For more information about kimono, see the useful notes. For specifically kimono-flavoured fanservice, both sexual and not so, see Kimono Fanservice.
Kimono is a likely wear-of-choice for Yamato Nadeshiko, and will underline her such qualities Up to Eleven. A Geisha, at least a proper one, will never work out of kimono. An elderly character wearing kimono will likely represent the traditional ways, demanding respect as the iron-fisted matri- or patriarch of their family. Sometimes the whole family is dressed this way, and might seem stuck in the Middle Ages when it comes to values.
If the fianceé or would-be-so is shown in kimono, expect her to be an upper-class maiden brought up in "Kyoto style", i.e. the old-fashioned way. In short, characters wearing a kimono daily means that they will most likely follow the expected ideal of a Japanese person of their age, sex and position. In a notable exception, however, a working age male daily wearer reads as somewhat of a rebel, as he most likely won't be a white-collar salaryman. Yet another character type seen wearing kimonos is certain hostesses — often a background hostess coupled with a dress-wearing one. In their case, the kimono belongs to their shtick of more grown-up, discreet charms and Yamato Nadeshiko or even geisha-like aesthetics.
In modern Japan, the skill of dressing up in a kimono and carrying it is largely limited to dancers, geisha and such, and aficionados. Being able to dress oneself up in a kimono is oh-so-WOW, while yukata-wearing skill is more like a citizen responsibility. Kimono are also not cheap by any means. Thus, daily kimono wearer characters have a certain aura of elite in the Japanese mind.
Note that simply wearing yukata does not qualify a character to be traditional in kimono — it's considered a different type of garment altogether in Japan, and has different connotations. Similarly on the opposite end, wearing an uchikake, i.e. a loose, unfastened outer kimono on top of the normal kimono, in normal conditions (outside weddings) multiplies all the traditionalness, class, and wealth indications the kimono itself gives to a character.
In Azumanga Daioh, of the six students and two teachers, only Sakaki and eleven-year-old Chiyo knew how to put on a kimono, and had to teach the rest. Kagura's parents bought her one for the occasion.
In Hidamari Sketch, not only does Hiro lend Miyako her old yukata, but it's mentioned that Sae put hers on like a guy at first.
In Ichigo Mashimaro, it's discovered that Ana doesn't have a yukata, so she temporarily "borrow" one off of Miu. As in, Miu had been wearing it when she borrowed it. Then Chika remembers Nobue's old one, which Miu ends up wearing to the matsuri.
In Lucky Star, the girls talk about the tying of the obi. Kagami's assumption was that Miyuki had tied it herself, but instead, the person at the store tied it. Konata's obi was tied by her father, a fact which disturbs Tsukasa.
Ryougi Shiki from Kara no Kyoukai wears nothing but kimono, except for a red leather jacket over it.
Kaibara of Oishinbo is a renowned artist who practices several traditional artforms, as well as a hard-line traditionalist in other areas and almost always wears a kimono. Older characters also frequently wear kimonos.
In Niji No Nataasha, Natasha's rival is Umeko, a very traditionally brought up high class girl, and you guessed it, she always wears splendid kimono. Her mother, practically a queen at home, never needs to lift a finger to get everything done (they have many servants), and she wears kimono + uchikake.
Lupin III has Goemon Ishikawa XIII, who is always seen in a kimono and hakama, reflecting his Samurai honor and traditional ways. (Except for the rare times that he wears a disguise)
The kimono is standard garb for Nozomu Itoshiki, the despairing teacher in Sayonara, Zetsubou-Sensei. Also for his stalker, Matoi Tsunetsuki, since she always dresses like her current love.
Also worn by his friend Ikkyu-san, who has a passion for all things old-fashioned.
On Quantum Leap, Sam leaped into a man who had a Japanese War Bride he brought home from his stint in Japan, and she wore a kimono all the time. The year was 1953. In the context, her constant kimono wearing might be related to either not wanting to give up clothes reminding of home and good pre-war times, and not needing to do so, or the production wanting to underline her otherness.
Samurai Sentai Shinkenger: The team wears traditional kimonos for some role-calls, and their ancestors wore them when not transformed.
In The Mikado, a play set in Japan, the cast is wearing kimonos. Specifically, the Three Little Maids are often in pastel shades of pink, blue, and yellow. The costumes are not even close to authentic in most productions, although this is often artistic license - the play is set in Japan but is, at heart, as British in its sensibilities as anything by Gilbert and Sullivan, and some productions lampshade this by blending British and Japanese elements in the costumes. In the original production, the kimonos were extremely accurate and well-researched, as was the case with most G&S productions. Gilbert wanted the sets and costumes as realistic as possible, to make the absurdities of the plot and jokes stand out in harsher contrast.
Early in Persona 4, the transfer student runs into Yukiko Amagi while she's wearing a kimono. It's used as visual shorthand for how she's following her family's traditions and becoming the next head of the Amagi Inn.
Gym Leader Erika always wears a traditional kimono. Four generations later, she remains the gentlest and most polite of all female Gym Leaders. She runs a perfume shop as her day job and tends to flowers as her hobby.
There is also a quintet known as the Kimono Girls. These are the only characters in the games from which they originate to keep their Japanese names (though mixed up among them). Their role is to perform an old ritual to bring Ho-oh to the top of Ecruteak City's Bell Tower. Note that the entire Johto region, where they live, has a strong feudal Japanese look, with old-fashioned wooden houses and paper doors, temples with guardian monks, and a culture deeply reverent of tradition.
Yuyuko Saigyouji wears one, being the ghost of a daughter of a noble family. Out of a huge cast of girls who all wear some kind of Elegant Gothic Lolita clothing, her outfit is one of the few that resembles traditional Japanese clothing.
Kotohime and Yuugen Magan (specifically the "core" section) from the PC-98 games also appeared in kimono.
Sakura Wars: When not in the field, Sakura Shinguji wears a kimono consisting of a pink haori and red hakama.
Dead or Alive: In all of her appearances so far, Ayame, Kasumi, Ayane, and Hayate's mother, is seen wearing a kimono.
Kokori Fushikawa from Maji De Watashi Ni Koi Shinasai almost always wears a kimono. She may be more of a spoiled brat than a Yamato Nadeshiko, but she holds on to the traditional values of the noble families well, mainly their superiority over the "commoners", and flaunts it at any chance she gets.
Cartagra and Kara no Shoujo are set in modernizing, postwar Japan. But Takeshiro (protagonist of Cartagra) and his wife are among the notable few who stick to traditional dress. In contrast with Reiji (protagonist of Kara), the two are less quick to adopt 'modern' styles and means, even though the wife is now a television actress.
Hiyoko Saionji wears a kimono as her only outfit during Super Dangan Ronpa 2, since she's a Japanese traditional dancer. However, it's later revealed that she's unable to tie her obi by herself.
In Tsunami Channel, Haruna is presented as a very traditional girl from an extremely wealthy and traditional family, having been groomed like a samurai wife (naginata wielding and all), so she naturally wears kimono all the time.