"Little Caesar," "White Heat" and "Angels with Dirty Faces" are among the greatest crime movies of all time. Electrifying performances all around. If you want to try an older classic that's off the beaten path, get "Key Largo." Edward G. Robinson's performance as Mob boss Johnny Rocco makes his portrayal of Little Caesar look like a choirboy. In fact, it's hard to think of any films that either Cag or Robinson made that weren't good.
I and others here (notably SC, plawrence and Apple, I hope I haven't left out others) are big fans of "Film Noir." Try "Laura," "Asphalt Jungle," "The Killing," "Out of the Past," "The Killers."