If you want a good *classic* gangster movie, there are some choices you may not have heard of but might enjoy. These are much older films which, when you watch them, you can see how influential they were:
Rififi (French,1950's)
This is more of a heist film, but I had to put it in, because it is such a classic, and it certainly has the criminal element, as well as the cops. One of the things that is so cool about it is the heist itself, still an interesting crime after all these years.
Le Samorai (French, 1960's)
The story of a hitman. The original anti-hero. Solitude, loneliness, the samorai code of honor. Melville also filmed other gangster movies, but Le Samorai is my favorite.
The original
Get Carter (British, early 70's) A very young Michael Caine, the brutal Brit underworld, absolutely brilliant dialogue.
Newer films, but IMHO modern classics:
The Coen Brothers'
Miller's Crossing. (American, 1990)
Two different (Irish) mobs, and divided loyalties.
Of all of gangster films, this might be my favorite, because it is so subtle and layered, plus it has a little old-time flavor to its dialogue.
The film does not feel epic like The Godfather, yet every scene is a set-piece.
Great ensemble of actors, and the movie has everything: action, mystery, suspense.
Honorable mention:
The Untouchables (newer version)
Lock, Stock, and Two Smoking Barrels
The Limey
Donnie Brasco
A Bronx Tale
Sexy Beast
I assume you've seen Scarface, The Godfather Trilogy, Goodfellas, Casino?
I especially liked Goodfellas.