Repo! The Genetic Opera has two of these as various points - Marni, who died before the film started, and her daughter Shilo, who inherited the disease. Until it turns out that she's not really ill—her father was poisoning her so she would have to stay with him.
October Sky features a kind and encouraging schoolteacher, Miss Riley, who is revealed to suffer from Hodgkin's Disease during the third act of the film, giving the Rocket Boys that extra emotional push to pull off their last, climactic, rocket launch.
Seeing as how October Sky was based off of the autobiography Rocket Boys (complete with the actual aforementioned Ill Girl), that automatically makes this trope into Truth in Television.
LoveHKFilm uses the term "terminal beauty" to refer to romance movies that feature one of these girls as the primary love interest, and features a good number of reviews of such Hong Kong movies in general.
The entire point of Nicholas Sparks' A Walk To Remember.
Satine from Moulin Rouge!, as mentioned above. An unusual example in that she remains ignorant of her condition until 2/3 of the way through the movie, and then tries to keep it a secret from everyone until the last possibly second. (Everyone but Christian, the Duke, the Duke's man Warner and possibly Toulouse and the Narcoleptic Argentinian know she's doomed.)
In The Constant Nymph, Tessa suffers from severe stitches and fainting spells caused by running or too much emotional stress...and when you're 14 and in love with a family friend who's much older, you have lots of stress.
Jennifer Cavelleri, in Love Story. Probably one of the Trope Codifiers in Western modern media, as her struggle with cancer and eventual death are still very iconic.
The female lead in the Taiwanese movie Secret. This is not the titular secret.
Sympathy for Mr. Vengeance by Park Chan-Wook (of Oldboy fame) seems to follow this trope to the letter. The plot is driven by the fact that the deaf-mute main character cannot afford the kidney transplant that his sick sister needs to survive. Abjectunrelenting horror ensues.
Grace in Excision. Her cystic fibrosis is the main reason why her sister Pauline wants to become a surgeon, which in turn gets Grace and another girl killed as Pauline tries to perform a lung transplant.
Jamie in Awalk To Remember. She has leukemia and found out when she was little. She doesn't want anyone to treat her differently, which is why she doesn't tell anyone at school. Or Landon, because she doesn't want him to be heartbroken if he falls in love with her
Jamie: I told you not to fall in love with me. Before she tells him about her cancer
In Akira Kurosawa film Scandal, Ichiro is convinced to hire third-rate attorney Hiruta as his lawyer after meeting Hiruta's sweet, innocent daughter Masako, who is bedridden and dying of pneumonia. Hiruta for his part is driven to betray Ichiro so he can get money to take care of Masako.
In M. Night Shyamalan's film The Sixth Sense, Kyra, a chronically-ill girl that visits Cole after she dies, was this during her lifetime, for a reason: her sickness was being prolonged by her mother, who was implied to be suffering from Munchausen's Syndrome by Proxy, craving the attention that having a sick daughter gave her. She poisoned Kyra with a household cleaning agent, and was beginning to do the same to her little sister following her death.
Assault on Wall Street: Jim's wife Rosie is recovering from a near-fatal brain tumor and requires expensive medication, forcing him to work around the clock to provide for her. This is also why he tries his darndest to keep their dire financial situation hidden from her. When she does find out, it drives her to kill herself.
Shadows of Forgotten Ancestors: Marichka is not very strong. She collapses during a festival from dancing too much, forcing Ivan to carry her away. She later loses her footing while trying to rescue a lamb and falls into a river.
Chopin in Impromptu, although during the period in which the movie's set he's only a bit delicate, not dying.
Doc Holliday and his friends were aware of his terminal condition (and the audience was reminded with his Incurable Cough of Death,) but it was less often cause for depression than morbid jokes and badassery. He also doubles as a Real Life example.
Eric Cruise, the main character from Mac and Me, is a little boy who's confined to a wheelchair. At the end of the movie not only he gets Back from the Dead by the titular Mac and his family, but he's healed and able to walk again.
Steve Rogers has a Long List of afflictions from asthma to rheumatic fever, in addition to general physical weakness and small stature. Then he signs up for the super serum experiment, and the restis history.
Tsarevich Alexei in Nicholas and Alexandra, afflicted with hemophilia, as was true in Real Life. He subverts the archetype since he thirsts for revenge against the Reds.
Nux, the sickly War Boy in "Mad Max: Fury Road", appears to be suffering from leukemia or lymphoma; he has tumors on his neck, gets fevers at night, and needs blood transfusions in order to even stand.
The plot of The Secret of NIMH revolves around Ms. Brisby trying to take care of her son Timmy, who has pneumonia.
In Con Air, Poe's Black Best Friend Baby-O is diabetic. One of the reasons Poe refused to leave the plane was getting the poor guy's insulin.