Just to add a few films "The General" about the Irish mob (in Dublin - not Hell's Kitchen) is a pretty solid look into organized crime though a bit too sympathetic and an unpopular view of its main character

"Little Odessa", is a little film with a look at the Russian/Jewish mobs of modern times in New York

"Running Scared" (2005) is a nice action composite piece with a lot of crime with a lot of ethnic groups and a lot of action...

"The Krays" is a fabulous film about organized crime in the east end - and "The Long Good Friday" touches on the relationship between the IRA and organized crime in Britain in a great way - one of my favorite movies of all time in fact.

"The Essex Boys" is a more modern take on organized crime in England and a story driven Sean Bean feature...

"Year of the Dragon" - drags on in some spots but is a pretty good take on Chinese Tongs in NYC