If you are asking for Hollywood movies, I would suggest Momento, One flew over the cuckoo's nest, Godfather, schindler's list. My favourite one is a Dexter (TV series) apart from Game of Thrones
If you are interested in other languages, Try The Intouchable (French - Comedy/Drama), Malena (Italian - Drama/Romance)
Indian Movies - You'll see a lot of cultural difference. Society is family oriented. You might not be able to accept the logics in these movies. But have a try with atleast one. I'm an Indian so my suggestions would be Vettaiyadu Vilayadu (Tamil-Thriller/Action) Rab Ne Bana Bi Jodi (Hindi - Drama/Romance) Premam (Malayalam - Drama/Romance) Bangalore Days (Malayalam - Drama/Romance) I (Tamil - Thriller/Romance) Bajrangi Bhaijaan(Hindi - Drama)