As the dominant mafia outfit in The Godfather trilogy, the Corleone crime family is constantly targeted by individuals or groups that either covet the power that the New York outfit has or are driven by their own selfish interests. Most of the enemies are easily terminated by the capable 'made guys' of the family but a few have been way too obstinate and vicious.
A decent number of the formidable foes are mob bosses too but others come from various fields since the family has diversified its interests. A couple of factors make these select enemies better than their counterparts, including their influence, general intelligence, and ability to cause harm. Some are arguably better characters than Michael and Vito too.
Archbishop Gilday
The shady Archbishop carries himself as a trustworthy individual but secretly works with Licio Lucchesi and Don Altobello to defraud wealthy, religious citizens. He even scams the intelligent Michael by making him deposit $600 million in the Vatican Bank.
Gilday is so shrewd that he takes advantage of Michael's desire to be closer to God in order to atone for his past sins. Unlike other enemies that opt for violence, Gilday differentiates himself by bleeding the Corleone crime family financially. He tricks Michael into investing in International Immobiliare, a real estate company in which the Catholic Church has majority shares. The Archbishop eventually pays for his sins courtesy of a bullet from Al Neri, but not before he nearly causes the powerful organization to go bankrupt.
Moe Greene
Based on the legendary mobster Benjamin "Bugsy" Siegel, Greene is the founder of Las Vegas. He begins feuding with Michael when the new Corleone crime family boss attempts to buy him out as part of his plan to set up shop in Nevada.
Greene is the biggest obstacle to Michael's expansion plan. The new boss understands that he can't dominate Las Vegas with its founder in the picture and that's why he attempts to get rid of them. Michael is obviously to blame for their enmity since it's he that makes forays into a territory that isn't his. Given how stubborn and influential Greene is, Michael has a hard time making inroads. Left with no other choice, he orders a hit on Greene as he is getting a massage.
Jack Woltz
The film producer is the founder of the fictional Woltz International Pictures, which dominates Hollywood. Out of spite, he refuses to cast Vito's talented godson, Johnny Fontane, in a movie, causing friction between him and the Don.
Woltz stands in the way of Vito and his desire to see his friends and associates succeed. He is extremely unreasonable and the only reason he refuses to cast Fontane is that an actress chose the young actor over him. He is stubborn too as he keeps refusing Vito's requests, forcing the Don to kill his favorite horse, Khartoum.
Carmine "The Milkman" Cuneo
The Cuneo crime family boss is the only Don whose activities have never drawn the attention of the federal authorities. He owns milk trucks in the Bronx that he uses to conduct illegal operations and is the second most senior member of The Commission.
Cuneo's lowkey nature makes him very dangerous since his enemies never see his attacks coming. When he colludes with fellow Dons to take down Vito's empire, his involvement is never established until later on. But just as all runs eventually come to an end, Cuneo meets his demise when Michael orders the deaths of all New York families at once.
Bruno Tattaglia
Tattaglia pretends to be Luca Brasi's friend but sets him up to be garroted by Sollozzo. He also assists the drug lord in planning the hit on Vito.
The major difference between Tattaglia and the rest of the enemies is that he isn't his own man. He is more effective as an ally. It's through his assistance that Sollozzo is able to cause so much damage to Vito's organization. And even when he gets killed, he doesn't stop being a problem. Barzini avenges his death by ordering the murder of Sonny.
Don Osvaldo "Ozzie" Altobello
Don Altobello starts out as a friend. He even becomes Connie's godfather after baptism. When Michael chooses to convert the family into the more legitimate Corleone Group, Don Altobello becomes disgruntled and attempts to murder him.
What makes the former ally such a great adversary is that he has a human weapon at his disposal. Altobello has the best assassin in the world at his disposal, the famed Mosca of Montelepre, who speaks in code and never misses his targets. The Sicilian assassin perfectly describes his hits for Altobello as "removing stones from the Don's shoe." Thanks to Mosca, Altobello hands the Corleone family one of its biggest blows by killing Mary at the Opera Cavalleria Rusticana.
Licio Lucchesi
The Italian power player conspires with Archbishop Gilday and Corleone crime family capo, Joey Zasa, to defraud Michael of $600 million. He has a great run before he gets stabbed in the neck with his spectacles in what qualifies as one of the best kills in The Godfather trilogy.
Lucchesi is portrayed as the master schemer. Apart from lessening the zeros in Michael's bank account, he has a couple of other accomplishments that confirm his status as a badass Don. He wipes out many of the powerful New York family's associates by ordering a submachine gun helicopter raid at a Commission meeting in Atlantic City. Moreover, he is so influential that he moves around with a team of police bodyguards everywhere he goes.
Emilio Barzini
Barzini grows from a lieutenant in Giuseppe Mariposa's organization to the chieftain of the Barzini crime family within a short span of time. Together with Sollozzo and Tattaglia, he conspires to bring down the Corleone crime family.
Barzini is a lot more intelligent compared to the other Corleone foes because he causes Vito his biggest loss by sending his men to ambush his son Sonny at the Jones Beach Causeway, (one of the most iconic locations in The Godfather). The hitmen spray Sonny with bullets in what has remained an unforgettable movie scene over the years. His wings are spread far and wide too as he has gambling and narcotics businesses in Las Vegas and Cuba.
Virgil "The Turk" Sollozzo
Virgil Sollozzo is also one of the more formidable foes the Corleone family had faced. After Sollozzo approached Vito with the proposal to partner with him, he made an attempt on Vito's life because the Don declines his offer (because he considers the drug trade immoral).
Despite not being as influential as Vito, Sollozzo is able to terrorize the Don and put numerous dents on his empire. Apart from trying to kill Vito twice, he murders his most capable enforcer, Luca Brasi, and kidnaps his consigliere, Tom Hagen. He is also cool enough to hire NYPD police captain McCluskey as his henchman. By the time Michael shoots him at the diner, he has caused enough injuries in the Corleone family to leave a lifetime of scars.
Hyman Roth
The influential mobster from Miami gets in business with Vito during the Prohibition Era but falls out with Michael when the former soldier takes over as the boss. He manipulates Michael's brother Fredo into working for him, but their treachery is soon discovered.
The most dangerous enemies are always the most powerful ones. Roth is so powerful that he is protected by the Cuban president Fulgencio Batista's government. Apart from being canny, he is extremely difficult to kill too. Michael tries everything. He even sends Bussetta, one of the best enforcers in The Godfather, to kill him at a Cuban hospital, but that attempt is thwarted by military personnel.