Muse from Romancing Sa Ga 3. Surprisingly enough, she is one of the better characters to recruit after she is cured of her sickness.
Subverted in Super Robot Wars Original Generation: Ryusei's mother is an adult Ill Girl, but it's due to a military project she used to work on as a psychic destroying her body. Her son has ended up being "recruited" by the same project in exchange for paying for her hospital bills.
Silent Hill 2 has Mary, a rare adult example. Naturally, she has the Incurable Cough of Death, too. The real rarity is the fact that she dies before the start of the game and is only seen and heard in flashbacks or maybe not.
Breath of Fire 3 subverts this during the Contest of Champions. Emitai, one of the competitors, visits the heroes before their bout (which is weighed against him due to its rules) and introduces them to his daughter; he claims to be in the contest to earn her an operation that will cure her disease, and asks them to throw the fight. As one of the heroes is being held hostage, they refuse. After the match, however, if you visit Emitai's dressing room, you learn that it was a giant fraud on his part to get his opponents to forfeit. Just to make this clear, after the midgame time skip, you can find Emitai again (and recruit him as a master); his daughter has grown up and is rather embarrassed with him.
In Advance Wars: Days of Ruin, Isabella/Catleia fills this role early on due to being infected with the mysterious floral virus. Will/Ed is the one to cares for her most, but because the virus only affects younger people, he'd be in danger if he was around her too much. Due to her strange memories, the crew manages to find a cure for it. Unfortunately, the virus later evolves to be able to affect matures as well.
Heather the Ghoul from the Vampire: The Masquerade - Bloodlines game practically embodies this trope. First, you have to save her life when she lies dying in a hospital. Then, when she finds you again, she acts so cute and affectionate, you just have to have a heart of stone to send her away. Then, she starts making you small presents and other pleasant things, like letting you feed on her blood, free of charge, etc. Most of her behavior is determined by her condition (by turning her into your ghoul, you bind her to yourself and your blood becomes a powerful, addictive drug for her) but that doesn't diminish her cuteness even one bit. Trust me. That she is a Meganekko and a potential Cosplay Otaku Girl doesn't exactly help, either... if you don't send her away, at some point she is gonna be kidnapped and murdered as an act of revenge upon you.
Subverted by Raquel in Wild ARMs 4. While she's slowly dying of an unknown disease in her body that's greatly implied to be radiation poisoning, it doesn't stop her from becoming a badass swordswoman and one of the most powerful characters in the game.
Fire Emblem has three cases:
In Fire Emblem 7, Dorcas's wife and Victorious Childhood Friend in an ill girl named Natalie, who has had problems in her leg ever since she was a little girl. One of the earlier missions is to keep her safe her inside of some abandoned ruins, and if Lyn talks to her husband who is in the enemy group, you can make him defect and join your group.
Tyler Chase's little sister Amy is infected with the Deftera GUILT two years prior to the first Trauma Center, and eventually goes into critical condition in Chapter 3. Derek operates on her and cures her, thus removing her status as Ill Girl.
Colette from Tales of Symphonia, who ends up suffering from a couple various ailments, the first being Angel Toxicosis Actually is pain from her soul being consumed by the Cruxis Crystal, as part of the World Regeneration Journey, and the second Chronic Angeleus Crystallius Inofficium actually does disfigure her (In the one cutscene where it's visible) and you spend a while (half of disc 2) getting the cure for her.
Cheria starts Tales of Graces like this, but she gets better when Asbel returns.
Tomoki in Canvas 2. However, the surgery she needs is actually quite easy and not that expensive. Not even that risky. She's actually afraid it will work and she'll be lonely.
Mary/Maki Sonomura in Persona is introduced as an Ill Girl, but when demons arrive to the scene, she suddenly got back up. Turns out this healthy Mary is the 'Ideal Mary', imagined by the real, ill Mary, who dreamed of her own world where one of the aspects there is that she's healthy, and by some complicated means, it's coming to take over reality.
Yasumi Aizawa in Aoi Shiro is one of these. Until it turns out she just needed a little blood.
Jessica from Mana Khemia: Alchemists of Al-Revis. One alchemist, who turns out to be The Hero's "father", sort of, cured her ... at the cost of her life energy. In short, she got better, but her life was cut in half at least.
Fana from Avalon Code. Interesting in that you can actually heal her by removing the illness code attached to her, but this requires a series of related plot events, as you can't just pluck out the code and slap it on something else (codes with this property are marked with spiked borders).
In the Tokimeki Memorial series, there's MioKisaragi of Tokimemo 1, who suffers from anemia and thus and can't handle violent physical activities and emotions, and Hotaru Izumi of Tokimemo 3, who had to stay for a long time at the hospital, and still suffers from some aftereffects, due to a car accident a few years prior the game's proper, which also cost the life of her dear boyfriend.
In Mitsumete Knight, the Spiritual Successor of Tokimeki Memorial, the resident Ill Girl is SarahPixis ; she suffers from a heart disease that prevents her to go outside, and the Asian (the player avatar) gets to meet her as his private teacher. Other Ill Girls are Sophia'sestranged mother and little brother, Dolphan's Queen, as well as Teddie Adelaide, Sarah's nurse and friend, who suffers from the same heart disease as her and thus why the two are close.
Yonah from NieR, who is infected with the Black Scrawl Virus, prompting her father/brother (depending on which version you buy) to go out and fight his way to finding a cure. Later on, it is revealed that Kaine is also infected.
Patchouli Knowledge from Touhou is really sick. She suffers from asthma, anemia, and Vitamin A deficiency because of her refusal to leave the library she lives in for centuriesnote and also because of all the poisonous chemicals that she uses for her magic. This is used to justify her inconsistent power level; when she's an Extra Boss in one game, she explains beforehand that her asthma has cleared up.
In the JRPG Lost Odyssey the player can acquire an ingame codex entry of the maincharacters past experiences. One in particular centers around an Ill Girl whom liked to hear his stories of far off places when ever he stopped by. The codex ends with the last encounter with this Ill Girl has her comatosed and on the brink of dying when he arrives to tell her one last final story.
Occurs a couple of times in the Growlanser series:
Growlanser II: The Sense of Justice includes Charlone's younger brother in this role.
Harvest Moon Magical Melody features a girl you can romance who is incredibly ill from some vague disease, and as such she spends every waking hour in the hospital, and you have to come visit her. You could always just woo her nurse instead.
Kaoru Watabe from The King of Fighters, who is in a wheelchair at the start of KOF'97. She has only started to take her first steps out of it by the time she meets her idols, the Psycho Soldiers. Around KOF 99 her health has improved dramatically, atleast enough to have her help the group out of the NESTS base.
In the Yume Nikki fangame .flow, through the game's symbolism, it is heavily implied that Sabitsuki, the player character, is dying from some sort of illness. This isn't just an Epileptic Tree, but almost canon. Maybe.
Maria Robotnik of the Sonic the Hedgehog series had SIDS. In fact, Gerald Robotnik's creation of Shadow the Hedgehog was his attempt to save Maria's life.
Growlanser II: The Sense of Justice has a female character whose younger brother is an ill boy. And yes, there is a mysterious "operation" that can cure him, and this provides that character's main motivation. In a slight variation on the usual plot, the character's family is very wealthy and can easily afford the operation, but the Ill Boy is afraid to go through with it because it is reputed to be extremely painful. (Maybe the Magitek of the setting doesn't include anesthetic?)
Then there's Prince Julius of Velthomer/Grannvale from Fire Emblem: Genealogy of the Holy War. In Thracia 776 he catches a high fever, and a conversation between his half-brother Saias and girlfriend Ishtar states that while he was somewhat delicate as a child, his health really declined after he became the vessel for the Dark God Loptyr.
In Fire Emblem: Binding Blade, Elphinaka Prince Mildain has really bad eyesight. He once was poisoned to near death, and this partial blindness is the only effect that still remains.
Subverted by Blazing Sword's Lucius, who is said to be pale and sickly. His companion Raven asks him once in a while if he's "under the weather", and he apparently has a borderline seizure in his C support with Renault, who also shows worry for his well-being. However, Lucius himself says it's not a physical illness, but one "from the soul". (It could be clinical depression or PTSD, as he says he tries to help others with their pain yet he is afflicted too.)
Played straight by Nils. At some point he does have a seizure and collapses, and his older sister Ninian asks the group not to move him from the spot he passed out on. The following mission has protecting him for 15 turns as its goal.
In the aforementioned Henry's supports with Olivia in Fire Emblem Awakening, he claims his bloodlust is a genetic nervous disorder. Whether it actually is or not, eh, it's something else. His profile, on the other hand, says that he actually has hypotension aka low blood pressure, which can potentially be quite serious.
In Mega Man Battle Network 3, a kid named Mamoru has an illness with a vague acronym (HBD) that essentially boils down to a heart defect. Lan helps the kid out and convinces him to go through another operation that is supposed to cure it because it just happens to be the disease that killed Lan's twin brother Hub, whose mind was digitized and placed inside Megaman.EXE. The hospital just has to be attacked on the day of the operation, and it's up to Lan to save everybody, including the kid.
Ion from Tales of the Abyss is known to have a weak constitution, and upon using a Daathic fonic arte, becomes weak to the point of collapsing. This is actually because the Ion seen in the game is a replica of the original Ion, who died a few years prior. Doing things such as using fonic artes or reading the Score cause Replica Ion's body to degenerate.
Emilio Juarez from Trauma Center: Under the Knife 2, who is one of the Sinners (read: tortured orphans used by the bioterrorist organization Delphi as lab rats) saved by Derek in the first game is seventeen, yet manages to be an excellent example of an Ill Boy all the same. If it weren't for all the "he"s and "boy"s used referring to him, though, it probably wouldn't be hard to mistake him for a more traditional example of the trope.
Marlin from the Harvest Moon games set in Forget-Me-Not Valley was an Ill Boy in his youth. He was moved out into the mountains in the hope that the air would cure him. It did help quite a bit, but he's still kinda sickly.
Similar to the above, Hanbei from Pokémon Conquest suffers from tuberculosis (not like the game will state that). Unlike the above example, he keeps it to himself and does what Hideyoshi tells him to do, so at the end of his episode, he starts coughing. When asked what's wrong, Hanbei responds that he got too excited; Kanbei doesn't believe it one bit.
Akinari Kamiki, the Sun Arcana from Persona 3, is a prospect writer who was born ill, thus his days have been numbered ever since birth. Developing his S-Link is about having him learn to enjoy his last days of life. He will die before the game is over, leaving the children's book he wrote with the MC's help and encouragement as a Tragic Keepsake, and if his link is maxed his soul will cheer on you before you take on Nyx.
The quarians from Mass Effect are a species of Ill People. Since their forced exile from their homeworld 300 years before the events of the games, quarian immune systems (which were already weaker than those other species) have deteriorated to the point that all quarians must wear environmental suits at all times just so they don't die. Every quarian Shepard meets in the games—from Wrench Wench party member Tali'Zorah to Badass marine Kal'Reegar to the valley girl complaining about her boyfriend on Illium—is one suit breach away from potentially deadly sickness. That said, they don't appreciate the stereotype:
"I'm not gonna die from an infection in the middle of a battle. That's just insulting!”
The main characters of Narcissu are a terminally ill boy and girl. The prequel adds two more ill girls to the cast, one of them an 8-year-old orphan. And the third game... just say the whole series revolves around this trope.