Goodfellas
White Heat
Bugsy
Little Caesar
The Public Enemy

I think of the GF Trilogy as a story of a family, with the Mafia as the defining milieu--but it's not a gangster movie per se. To make an analogy: "Gone With the Wind" is a movie about a family with the Civil War as a defining milieu--but it's not a Civil War movie per se. "Mean Streets" almost made my list--a very great film that's even better than "Goodfellas" in some ways--but
I think of it more as a story about friendship than about the Mob.