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]: Commits suicide by shooting herself in the head after waking up to discover that Leonardo DiCaprio has taken poison. (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)