For me, Goodfellas is the best gangster film I've ever seen. It really does stay with you long after it's over, made the more powerful because so much of it really happened.
While the Godfather I and II are more stylized, they're also remarkable. Great characters and subplots too.
I like Casino very much, but I never really liked the Ginger subplot(s) as much as the rest of the film.
No one has mentioned another one of my favorites: The Usual Suspects. Not a "mafia" film but absolutely about gangsters.
We might as well include Kill Bill Vol. 1 here too. It's my favorite QT film.
Someone mentioned Fargo. I wouldn't call that a gangster film so much (the criminals are all too stupid and disorganized to be "gangsters"), but it is extraordinary. One of the best films I've ever seen.
Just my view, but I believe Scarface is the most spectacularly overrated film I can think of. It has not aged well. So over the top and downright silly. Sosa is the only character in the film I like, and he's king of the bad guys. Have never understood why this film was such a cause celebre.
