Eerie, beautifully shot and perfectly paced, 'No Country For Old Men' is an undeniably excellent piece of work, not to ever be forgotten. Not to mention Anton Chigurh, one of the greatest, most intimidating screen presences ever to come into fruition.
Arguably the best film of all-time, 'The Godfather' is every bit as good as its proclaimed to be, and one of the best films ever made in terms of being technically proficient. The details are masterfully depicted, and the in depth examination of this Italian crime family is as realistic as it gets.
Believe it or not, there is a fine line between each of those genres/sub-genres. For instance, Die Hard contains crime. However, its a bonafide ACTION film. Everyone knows that. it simply wouldn't fit in here. You can find those types of movies in my other lists. The crime genre is a genre entirely on its own.
The 'Gangster' genre is self-explanatory, as well as 'Mafia' themed films.