One of the most beautiful (and, of course, creepy) scenes from Ridley Scott's Hannibal. The song playing is called "Vide Cor Meum" - composed by Patrick Cassidy. Scott also used it in Kingdom of Heaven.
Ellen Burstyn's much-lauded monologue from Darren Aronofsky's Requiem for a Dream. I've also included the reaction of Harry (Jared Leto) afterwards in the cab because it's entirely appropriate and just perfect.
The final scene from Jean-Pierre Jeunet's Oscar-nominated film, A Very Long Engagement. This scene features the two protagonists, Mathilde (Audrey Tatou) and Manech (Gaspard Ulliel), being reunited - it is one of the most beautiful scenes in the entire film, and given the stunning nature of this movie, that's saying something.
In this scene, from Christopher Nolan's 2002 thriller Insomnia, Detective Dormer (Al Pacino) interrogates the boyfriend (Jonathan Jackson) of a recently murdered girl. This is the audience's first look at Dormer's style of investigation.
Richard Hart (Bill Nighy) confronts his wife, Sheba (Cate Blanchett), after finding out about her affair with a 15-year old student of hers -- from Richard Eyre's 2006 film Notes on a Scandal.