Claire Danes

Film Deaths

Little Women (1994) [Beth March]: Dies of a heart condition, with her sister (Winona Ryder) at her bedside. (Thanks to Mandy and Hailey)
William Shakespeare's Romeo + Juliet (1996) [Juliet Capulet]: Commits suicide by shooting herself in the head shortly after both waking up from her feigned death and watching Leonardo DiCaprio die from the poison he consumed (due to him believing Claire had died earlier). (See also Olivia Hussey in the 1968 version.)
It's All About Love (2003) [Elena]: Playing a character who is cloned, she dies four times: Three clones are shot to death while ice-skating, and the original "Elena" freezes to death (along with Joaquin Phoenix) in the wilderness. (Thanks to Anonymous)
Stage Beauty (2004) [Maria]: Suffocated with a pillow by Billy Crudup in a play-within-the-film sequence; it's suggested during the scene that he might be angry enough to actually be killing her, but it does turn out to be just part of the play. (Thanks to PortsGuy)