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.)
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.
Bastian's mother in a flashback in The Neverending Story 2. And her death has driven a huge wedge between Bastian and his father.
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.
Chopin in Impromptu, although during the period in which the movie's set he's only a bit delicate, not dying.
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.