One of the only films i've ever thought as a "masterpiece" was Donnie Darko, probably a Thriller, if you haven't seen it please do! Really makes you think, very well made, and the ending just made me "wtf, wow, wtf, wow, wtf?" for a few hours.
The Green Mile. is apparently very good (i've only read book though, which is amazing

) Set on death row, the story of, basically, a big black man ("John Coffey, but not like the drink") sentenced to death for the rape and murder of 2 young girls. Drama? probably.
Shawshank Redemption, feels like a long film but gripping, set inside a prison, Drama i guess.
Pulp Fiction, Action, interesting filming style, funny in dark humour way a lot.
I'll post more later when i've more time.