Warning supreme taste incoming.

Monster is a psychological thriller and is my favourite anime by far, it has it all good plot, good characters, good music, not too short, accurate history and keeps you entertained all the time and combines them for an excellent experience. It's an anime that's almost flawless imo. First 3 episodes are rather slow though, but after that prepare for one hell of a ride.

After that I would say Kaiji another psychological thriller with another uncommon art style that is about gambling, desperation and the human mind. It grips you from the very beginning.

Well if you like thriller give these two a try, they belong to the best in that category.