Giuliani’s fight against organized crime needs to be understood in terms of his innovative use of RICO, the Racketeer Influenced and Corrupt Organizations Act (18 USC § 1961-1968).
In the 1950’s and 1960’s, especially when Bobby Kennedy’s Justice Department took organized crime as a public priority, the feds quickly found that they could easily arrest virtually any member of the mob they wanted, but they had enormous difficulty tying its leaders to the crimes of their underlings. See for example the Appalachian Meeting of 1957, in which some 60 bosses from various families were arrested and charged, but all their sentences for conspiracy to obstruct justice were overturned on appeal (note for later: before 1957 very few Americans believed the mafia even existed. J Edgar Hoover had even actively denied its existence, which suited the mob perfectly well). The problem was that traditional Anglo-American common law required more evidence for inchoate crimes than could be gathered, particularly in the face of the mafia’s code of silence.
Enter RICO, which passed in 1970. RICO allows prosecutors to bring charges against a member of an organization for the enumerated crimes committed by any other member of that organization. Importantly this means that bosses could now be charged for the crimes of the capos and soldiers. Throughout the 1980’s it was used very effectively to prosecute the mid and high level ranks, and did damage to the New York families. However many prosecutors remained wary of it for some time, given how new and potentially unwieldy it could be (the first RICO case came to trial in 1979, 9 years after its passage).
Thus, many high ranking bosses went untouched. But Giuliani realized that RICO’s definition of an organization could be extended. RICO defines a criminal enterprise very broadly and very extensively; it can contain factions of La Cosa Nostra, your grandmother’s bridge group, a labor union... just about any association of people, official or otherwise. Giuliani realized that the families were close enough in their cooperation with one another that they could all plausibly be tied together as one single criminal organization. The very concept of the mafia was itself an enterprise, and the bosses merely represented subdivisions of it. Most famously, eleven such leaders were tried together in the so-called “Commission Trial” (the Commission being the name of the panel of family leaders who periodically met to discuss business). Nine of the eleven were found guilty and sentenced to effective life sentences.
This was indeed a great blow, but its greatest impact on the subsequent power of the mafia was (arguably) indirect. The trial meant that RICO had finally reached its full potential (today it is perhaps the most powerful tool available to federal prosecutors). The mafia went even further underground than before, and generally abandoned any activity that would bring them unwanted attention (particularly public acts of violence). Ask any average American today if the mafia still exists and they will probably say no, or shrug at most. That is exactly the response the families want; to return to the days before the Appalachian Meeting when they were more of a scary bed-time story than a real threat. The Commission allegedly still meets, though nobody knows where or how often. From a legal perspective, Giuliani’s prosecutions are more laudable for the innovative use of RICO rather than for their impact on the mob.
Today, a variety of NYC public offices still work hard to fight the mob, albeit in a more regulatory manner. The Port Authority Police and the Waterfront Commission keep them out of the docks, the Business Integrity Commission keeps them out of waste management, and federal prosecutors still bring the occasional case (note in particular the creeping presence of corruption into the heating oil business over the last decade).
Sources:
Raab, Selwyn (2005). Five families: The Rise, Decline, and Resurgence of America's Most Powerful Mafia Empires
DeStefano, Anthony M. (2008). King of The Godfathers
Bernstein, Lee (2001). The Greatest Menace: Organized Crime in Cold War America
Reavill, Gil. (2013). Mafia Summit: J. Edgar Hoover, The Kennedy Brothers, and the Meeting That Unmasked the Mob