Yes, Elena. It's an excellent topic!
Travis, your name makes me remember another outstanding movie: Táxi Driver, by Martin Scorsese. The main character calls Travis Bickle.
To help the discussion I'll give more five options, but I could say many others.
The Mirror (Zerkalo), by Andrei Tarkovsky.
One of my favorites! A non linear story of a man in differents moments of his life. A movie that says much about the author's life. The movie has gorgeous scenes, as several movies of the same author: Stalker, Nostalghia, Andrei Rublev, Solaris, etc.
Iran | France
The Wind Will Carry Us (Bad ma ra khahad bord), by Abbas Kiarostami.
Kiarostami did great movies and this is one of them. Beautiful landscapes and a full of meanings story. A man who goes to the iranian kurdistan to find a dying old woman. I really like iranian movies!
Macedonia | France | United Kingdom
Before the Rain, by Milcho Manchevski
A movie in three mixed parts (Words, Faces and Pictures) that talk about unsuccessful loves and violence. A interesting story with good scenes.
Germany | Austria | France | Italy
The White Ribbon (Das weiße Band - Eine deutsche Kindergeschichte), by Michael Haneke
Haneke has strong movies. He likes to bring subjects that many other don't have courage to say, like he did in The Seventh Continent, Benny's Video, Amour, etc. The White Ribbon is about mysterious events that generate a widespread distrust in a community.
France | United States
Mulholland Dr., by David Lynch
It's another outstanding movie! I really like! It talks about dreams and jealousy. It's impossible to describe. It's a movie that allows many understandings. Lynch has others very good movies, as Eraserhead and Blue Velvet. He also has a pretty good TV Serie: Twin Peaks.