Actually, they never went away but a few prosecutions convinced a naive public that New York's five Mafia families were magically vaporized.
The FBI now is ringing alarms that "the city's Cosa Nostra . . . is more powerful than it has been in years" as reported by The Wall Street Journal: "unlike the in-your-face approach that media mob star John Gotti adopted in the 1980s, today's mafia has reverted to its roots and tried to become as invisible as possible, officials and experts say."
Further reading that may be of interest: