Ophelia kills herself because the fate of Denmark is placed on her shoulders when she is asked to more or less spy on Hamlet, her father has been murdered (by her former lover no less), from the confusion created by her father and brother with regard to the meaning of love, and her suicide is even an act of revenge.
How did Ophelia really die?
In Act 4 Scene 7, Queen Gertrude reports that Ophelia had climbed into a willow tree (There is a willow grows aslant the brook), and that the branch had broken and dropped Ophelia into the brook, where she drowned.
Does Ophelia kill herself in the movie?
In the movie, Ophelia does not die. Instead, after realizing that Hamlet's quest for revenge against King Claudius could prove hazardous to her own health — and deducing that she is pregnant with Hamlet's baby — Ophelia fakes her drowning death.