|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.
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]: Strangled 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)