Simply put, the Cute Ghost Girl is a female member of the cast who just so happens to be a ghost. Despite this fact, they often look entirely like a normal person (except for the presence of Ghost Lights and a lack of feet), will act accordingly, and are treated more or less normally by the rest of the cast. The whole "they're dead" aspect is not considered a big deal by anyone, and once they are inducted into the cast the fact that they are a ghost will only come up on occasion. Oftentimes, it can be easy to forget that they're a ghost because they act so much like the rest of the cast... to the extent that the cute ghost girl herself is sometimes afraid of ghosts.
In some cases, the ghost girl will actually have some sort of artificial body that allows them to act even more like a normal human.
A subtype of Cute Monster Girl. Often overlaps with Reluctant Monster, especially when they are first introduced. If the Cute Ghost Girl is evil and trying to scare the crap out of/curse everybody, she's a Stringy-Haired Ghost Girl.
Oshizu from To Love-Ru. Has an artificial body made by Mikado-sensei that she possesses.
Sayo Aisaka (seen above) from Mahou Sensei Negima!. A little more "ghostly" than others, but mainly because nobody can see her. When they finally figure out she exists they start treating her like a normal girl. Currently possesses a Voodoo doll and pilots this.
YuYu Hakusho has Sayaka, an Ill Girl who was desperate to have some kind of fun before she went to heaven. Botan plays the trope a bit more straight, despite being a Shinigami instead of a ghost. There's a scene in the manga where she has to rush back to Reikai, and Yanagisawa freaks out because her body suddenly falls over—what he doesn't see is that she's left it behind and is flying away on her oar.
In the anime, Sayaka's story was different. She was still a Cute Ghost Girl, but actually was an employee of Koenma who has to keep Yuusuke on check to see if he's really worthy of being revived.
Orihime was one of these in Bleach's pilot chapter, and if you don't think that tiny!Rukia is adorable as well, there's something wrong with you.
The Ranma One Half episodes with Kogane, although it is obvious she's a ghost. Also, when the negative energy from Ranma's female persona was released, she became a female ghost. This has led to some confusion since when the positive energy from Ranma's female persona was released, she was clearly alive. Both seem to share Ranma's memories, but seem separated from them.
Hanyuu (also known as Oyashiro-sama) from Higurashi no Naku Koro ni. Although she contributes to the ominous atmosphere in the first season, once she actually appears onscreen, she's revealed to be more of a MoeSpirit Advisor who fits this trope perfectly. Until the final chapter.
Ichiko from Otome wa Boku ni Koishiteru. She's actually an Ill Girl who once was in love with Mizuho's dead mother, and after dying she kept haunting the room they shared at their boarding school.
Misao from Asura Cryin'. Though she's not actually a ghost ghost, she's close enough.
Everyone who has an Asura Machina also has one.
Arashi and Kaja from Natsu No Arashi. While they actually are ghost girls, to the uninformed, they display no signs of actually being dead. Later on, another two girls called Kanako and Yayoi are introduced, and are revealed to be ghosts as well
Panyo Panyo Di Gi Charat finds the girls helping one who has the Ghostly Goal of learning to ride a bicycle — she apparently needed and failed to for a part when she was a child actress in life. It's not outright revealed that she's a ghost until the end of the episode, but there's mention of the studio being haunted beforehand that might lead the viewer to suspect.
Omiyo from Sgt. Frog. In one chapter, she has Fuyuki examine a photo for possible ghosts, which is hardly the strangest thing that happens in the house.
Kagome meets one of them in InuYasha. The girl's name was Mayu, her little brother was Souta's best friend and was in the hospital, and Mayu herself died in a fire (the same one that let her brother hospitalised) after a huge fight with her mom, thus her spirit was poisoned by hate and anger and couldn't rest in peace. Kagome has to save her from going to Hell due to her rage.
Chapter 29 of Ai Kora has Maeda and Shibusawa hunting one down: Maeda's interest is piqued when he finds the ghost girl has a really sexy back. Seriously, he's just that kind of guy.
"Ghost Princess" Perona from One Piece is an interesting variation. She isn't dead, but she has the power to leave her body as well as create various ghosts to attack with.
A few in Urusei Yatsura, all of whom Ataru flirts with. Nagisa is the most notable, being a Wholesome Crossdresser and thus a gender flipped version. The cast figures out that he's a boy only because Ataru and Mendou start to wonder why they're not flirting with Nagisa. He soon gets a physical form and romantically pursues fellow crossdresser Ryunosuke, his fiancée.
Mayoi Hachikuji of Bakemonogatari. The fact that she's a ghost is only ever mentioned in one episode.
Alice McCoy of Digimon Tamers might be one—it's never made clear whether or not she's dead.
Koko Wa Greenwood had a one-episode character of a girl who died prior to getting to date and is determined to have a good date before she passes on. She has so much fun that she decides to stick around at the end of the episode.
Jolokia-tan in Habanero-tan. It's a Stealth Pun, as naga jolokia is also known as "ghost pepper".
CLANNAD has Fuko Ibuki who, despite not actually being dead, is still not exactly... well, basically, the real Fuko Ibuki is in a coma, while her "ghost" of sorts is running around at the school. For a time, Tomoya refuses to believe it, thinking that it must be someone else claiming to be her, but it ends up being true. Thanks to the Cosmic Reset, however, she gets better.
Okinu from Ghost Sweeper Mikami. She comes back to life eventually, since her lieless body is found uncorrupted and still in use..
The Zashiki Warashi that lives in Japan's home in Axis Powers Hetalia. It's all but stated that she and the Kappa have to leave, though, since Japan cannot see them anymore.
Dee Ensy Stratmitos from from Kami-sama no Inai Nichiyoubi. Although she's not actually dead, and she manifests as a ghost in the outside world because she can't physically leave the sealed city of Ostia.
Young Justice had Secret, a sweet and naive ghost girl who showed up in a prequel issue and stuck around. She later becomes human, again.
The Perhapanauts has Molly, a cute ghost girl who works with a team of paranormal investigators. She died under unfortunate circumstances and is very uncomfortable discussing her condition.
The eponymous ghost in Anya's Ghost is a nice, polite little spirit, wearing an old-fashioned dress and poofy 'dandelion' hair. Of course, she's not quite so lovable after she goes all Yandere on Anya...
In Lucifer, murdered schoolgirl Mona continues her Romantic Two-Girl Friendship with Elaine, with the fact that she's dead being a comparatively minor thing once they take revenge on her murderer. She can't be seen by normal humans, but the entities who are aware of her treat her with the same level of respect/contempt they would have for living humans.
In Charlie St Cloud, Tess is a cute ghost girl, except that her body is dying, not fully dead.
Bones of Faerie: The main character, Liza, has her baby sister come back as a shadowy ghost.
Madison Avery: Main character, Madison, is a ghost and fairly cute (to some readers) to most people.
In The Lovely Bones, as well as The Film of the Book, the main character becomes this early on. As this is the focus of the book, more attention than usual is paid to the fact that she's a ghost.
Jane Thayer's Gus Was a Friendly Ghost series is a rare male example. Gus seems to have always "lived" in the attic of an old house (later converted to a museum), and the people he interacts with have no real trouble accepting him as a roommate.
At least one Limerick that goes, rather naughtily:
There was a young man from the coast Who had an affair with a ghost- At the height of orgasm, Said the pallid phantasm, (alt. "This she-ectoplasm") "I think I can feel it, almost!"
Live Action TV
Thelma in Hex is a prime example of this character type.
Komachi from Madan Senki Ryukendo. She's a ghost that only Kenji can see most of the time, and when she temporarily regains her body in one episode, she ends up faceplanting into the wall, since she can't walk through it anymore.
Annie from Being Human. The fact that she is a ghost is brought up a bit more often than average, seeing as how the whole premise is "monsters as roommates," but in a lot of her scenes she's just a normal female roommate who happens to be dead. And she definitely counts as cute.
Kyra in The Outer Limits episode "The Beholder", though she was an alien that was "out of phase".
Another episode has a woman's experiment leave her disembodied and her body in a coma. This being Outer Limits, she totally dies for real by the end, as does her husband who is trying to get the machine to restore her. It's made as un-depressing as such an ending can be - unusual for The Outer Limits, which almost always went for dark twists - by having them appear in spirit form and reunite, before vanishing for parts unknown but seeming optimistic about it.
Sarah Collins on Dark Shadows first appeared as a ghost, mostly to young David Collins, and in fact became his friend. The few other people she appeared to usually thought that she was just a regular little girl (budgetary constraints of the show prevented her usually looking particularly "ghostly" aside from her late-eighteenth century attire.) She was cute (if sometimes annoying, pretty much constantly accompanied by her theme music, "London Bridge," and usually bouncing a toy ball) and was also later instrumental in helping Maggie Evans escape from Barnabas Collins, Sarah's cursed vampire brother.
Maya Amano's ghost-girl in Persona 2. She's the most adorable little girl as a human, but admit it, the sailor outfit is twice as precious in 'transparent blue'.
In My Sims, you might get to see a Cute Ghost Girl named Cassandra wandering around town. She is also the only source of the rare Ghost essence, which she'll drop if you be nice to her. Oddly enough, you can plant a Ghost essence and it'll grow into a Ghost tree that drops more Ghost essences.
And in The Sims 3, you can get a (male) ghost to have sex with one of your (female) sims, then having a 50% chance of having a ghost kid as one of your sims. You can also make them have kids with another ghost, but for that you'll need some cheating.
Then there's Lolita Goth from The Sims3, who is also prone to Wild Mass Guessing. She's not in the Goth family tree, but she's arguably one of the favorites in the game.
One of the playable characters in the PuyoPuyo series is Yu, an energetic ghost girl. Later games pair her up with her twin brother Rei, who, while not nearly as energetic as his sister, is just as cute and harmless.
RosenkreuzStilette Freudenstachel has Rink Refraktia, who uses her sister Lecht's ability Falschgestalt to appear alive. It's very useful when defending her from various threats, especially against the likes of Freudia.
Unlike Minerva has Nina, the library ghost who is mildly fixated on the protagonist Brisbane. It's left ambiguous, though, as to whether she's actually a ghost or if she just grew up in the crawlspaces of the library.
Shion from Experimental Comic Kotone goes one step further, actually being able to pass for living...when she remembers to use doors.
Bryony, the deceased sister of Bear and Patches, more or less fits this trope in Catena. Most of the cast isn't actually able to see Bryony for quite some time. She's actually an angel (complete with pink wings).
Aranea of Homestuck, formerly. Also potentially any of the female players who could be considered cute, since practically everyone has died in an alternate timeline at some point, which means that those versions of them can be encountered in dream bubbles.
Karin-dou 4koma: Ran starts out as the vengeful ghost of a girl who was raped and murdered on Halloween. Seren confronts her after she kills a psychopathic pedophile and forcefully convinces her to drop her grudge and become a Cute Ghost Girl instead.