There is a tradition of glorifying the gangster in American culture. The Godfather Trilogy and the Sopranos are some of the obvious examples of the Italian-American variety but more recently the African-American Gangster culture has had it's fair share of glorification. Hip-hop and Rap videos are dripping with the ostentatious glamour that showcases gangster/drug dealer/pimp lifestyles.
American Gangster starring Denzel Washington is somewhat of a hybrid. It's the story of a poor African American who makes it big in the world dominated by the Italian American Mafia of 1970's New York. It's so natural to elevate the criminal element because criminal activity is so structurally similar to business activity. America admires the entrepreneur for his audacious confidence and his ability to struggle against risk in order to arrive at success. Frank Lucas (played by Denzel) is a perfect example of a man that possesses a combination of fearlessness, strength and innovativeness that allows him to reap the reward of fantastic riches.
Most Americans do not really feel like they have access to the opportunities to succeed in their lives. Criminal activity allows the fantasy of bypassing that difficult process of education and hard work and going straight to the riches. Of course it's just a fantasy since most of those who choose the life will soon end up dead or in prison. But Hollywood is in the business of selling fantasy and they do a pretty good job of it. Despite the occasional display of psychopathy, Denzel's portrayal of Lucas is mostly sympathetic. Lucas did end up in jail and penniless but it seems a small price to pay for someone who sees no hope for the future.