The Grand Theft Auto series are the best specially III and Vice City.

Max Payne and Max Payne 2 (still not available fro Ps2)

Mafia. PC now but will be released in PS2 soon.

True Crime: streets of LA is mob related, you play a cop (like in Max Payne)

Hitman.

And Gangsters 2, simulation.

Giorgio Luigi Gambino