Vice City is a place full of gangs and crime organizations that control the city's criminal factor in large scale. Some organizations are more powerful and relevant than others, but there are 8 specific organizations that directly interfere in the story in Grand Theft Auto: Vice City, for which reasons, classified as the most powerfull organizations in the city, but there are more than just 8 gangs.
Major Gangs
Vercetti Gang
Also known as Vercetti Gang Family, the Vercetti Gang is a powerfull criminal organization based on Tommy Vercetti's bussinesses and properties, but Vercetti Estate can be considered as their HQ, since it is where the gang starts appearing after the death of Ricardo Diaz by Tommy in 1986.
Their leader is Tommy Vercetti, with high ranking associates like Lance Vance (Until his betrayal) and Ken Rosenberg (Until 1992) and associates like Avery Carrington.
They are friendly to Tommy even when attacked, but are agressive and territorial with other gangs, even with the Cubans and Vice City Bikers, which are friendly to Tommy and involved with him in the storyline.
After the events of the game, they are considered to be the most powerfull criminal organization in Vice City, since the Forelli Crime Family, the main enemy of the organization, was weakened by the death of it's Don, Sonny Forelli, by Tommy.
Forelli Crime Family
The Forelli Crime Family is a mafia family based mainly in Liberty City the Don of the family beign Sonny Forelli, but by 1986, their best moment (implied to be the most powerful mafia family of Libery City), the Don, Sonny Forelli, decides to "move down south" to Vice City, sending Tommy Vercetti, that just got out of prison (since 1971, after an ambush prepared by Sonny to kill Tommy) and Ken Rosenberg to make an important deal with the local crime organizations.
Long story short, the deal with the Vance brothers, organized by drug lord Juan Cortez, gets ambushed by Ricardo Diaz's goons, only Tommy, Ken and Lance Vance survive after Tommy loses both the drugs and money from the deal.
Tommy promises Sonny to get back the money, throughout the game, Sonny will call Tommy to threat him.
Near the end of the game, Sonny will send goons to "tax" Tommy's bussinesses, beating up Earnest Kelly, because of that, Tommy personally kills the goons.
Sonny comes personally to Vice City to take the money from Tommy, because of Lance Vance, Sonny is warned of the plan to give Sonny fake money, due to this, Sonny faces Tommy, resulting in a shooting at Vercetti Estate, which ends in the deaths of both Lance and Sonny at hands of Tommy, ending the storyline and Forelli incursions "down south".
They don't appear roaming through Vice City and are only seen thrice in the storyline and only twice in gameplay, on which they are aggresive, in fact, they are counted as Streetwannabes in the in-game stats, but they are a key aspect of the storyline.
Diaz's gang
Ricardo Diaz's drug cartel, known in the in-game stats as Diaz' Gang, was a powerfull colombian cartel with it's base of operations in Vercetti Estate, before Tommy took it over.
They may be associated or even beign the same cartel as Gta III's, Colombian Cartel, since some of their members in GTA Liberty City Stories mention that they used to own a mansion in Vice City.
Back in Vice City, by 1984 they are the most powerfull organization in Vice after the decay of the Mendez Cartel by Victor Vance and Lance Vance. By 1986, Diaz, angered by the fact that the deal between the Vance Brothers and the Forellis was organized by Juan Cortez and not him, he send 3 goons to ambush the deal, killing Victor and 3 Forelli goons, but letting escape Lance Vance, Tommy and Ken Rosenberg.
Ricardo give Tommy some misions and also gets work for Lance Vance, who gets in the organization with a different name. After some missions, Lance tries to kill Diaz before Tommy was ready, so he tries to do so alone, failing and getting tortured by Diaz's goons.
Tommy saves him and together they assault the mansion, finally killing Diaz.
After that, Diaz's gang disappears from Vice City, beign replaced by Vercetti gang members, ending their influence in the city.
Before they disappear, they are completely neutral to Tommy, will only attack in self defense and will fight the Patrol Invest Group if they get on the mansion grounds, all this in free roam, they are only aggresive in a few missions and in rampages.
Cubans
The Cubans (also known as "Los Cabrones" in Gta Vice City Stories) are a street gang conformed mainly by Cubans, (with few exceptions like Tommy Vercetti, which after doing all of their missions is considered an equal), with their turf beign mainly Little Havana and their leader being Umberto Robina.
By the events of 1986, the Cubans are involved in a war against the Haitians gang to be the dominating gang in Little Havana, after some time, Umberto Robina, contacts Tommy and hires him to help him in the war against the Haitians.
After doing some missions for the Cubans and damaging the Haitians, Auntie Poulet, haitian gang leader, drugs Tommy and makes him work for her and the Haitians, damaging the Cubans this time. After some missions, Auntie Poulet would call Tommy to tell him that she doesn't need him no more.
Tommy then goes back to the Cubans and blows up a drug factory of the Haitians after a shooting with Cuban gang members and Haitian gangs member, beign the Cubans the winners and destroying the factory, after this mission, the Cuban-Haitian Gang War missions are ended.
Even though the final mission of both gangs is in favor of the Cubans, Haitian gang members will keep spawning in Little Haiti and sometimes in Little Havana and will fight the Cubans when seen, so it is implied that they were severely weakened, but not destroyed.
Them, along with the Vice City Bikers, are the only 2 gangs that don't get beaten up by Tommy in the storyline and will only attack Tommy if he atacks first or hijacks a cuban car, even though they should be "allies", the Vercetti Gang members will shoot the Cubans on sight.
Haitians
Like the Cubans, the Haitians are a street gang conformed solely by haitians, (since there is no known members of the gang that aren't haitian), their turf is mainly Little Haiti, with interests in Little Havana, their leader is Auntie Poulet.
By 1986 they are at war with the neighboring gang, the Cubans, for domination of Little Havana.
After Umberto Robina employs Tommy to help the Cubans against the Haitians, Auntie Poulet drugs Tommy and makes him work for the Haitians against the Cubans. After some missions, she will tell Tommy that she doesn't need him no more.
That was an error, because after the last Haitian mission, the last Cuban mission consists on blowing up a Haitian drug factory, which is a success, severely weakening the Haitians, but not destroying them completely.
Before the last cuban mission, the haitians are neutral and will only shoot if shot first or hijacked, but after the last cuban mission, they will shoot Tommy and his gang on sight.
Vice City Bikers
The Vice City Bikers is a Motorcycle club, based mostly in Downtown Vice City in 1986, specifically in the Moist Palms Hotel (members roaming outside, but not everytime) and their HQ possibly beign their club house, The Greasy Chopper. 2 members could be seen in the Pole Position Club, but they are probably just hanging around. Their leader is "Big" Mitch Baker.
Mitch describes themselves as "the biggest family of misfits, outcasts and badasses". The main difference between the Bikers and other gangs, is that they're the only gang that uses motorcycles instead of cars.
In 1986, Mitch meets Tommy when Tommy asks for protection during the Love Fist concert, but before the Bikers can give protection, Tommy must become one of his own, doing missions for Mitch, like racing other Bikers and steal Mitch's bike from the Sharks. After Tommy steals back the bike, Mitch will call Tommy telling him that he has the protection for the concert, and here ends the Biker's missions in the storyline.
The Bikers, along with the Cubans, are the only 2 gangs that don't get beaten up by Tommy in the storyline, even though they are supposed to be "allies", the Vercetti gang members will shoot Bikers who roam around.
Patrol Invest Group
Also refered as PIG, they are mainly a legitimate security force part of DBP Security , but they are involved in a few illegal protection bussiness with the Vice City Triads, on their legal operations, they patrol mainly yhe North Point Mall area, Escobar International Airport, Leaf Links Country Club, and Starfish Island, which could be considered their turf.
Even though they don't seem like a gang, the in-game stats classify them as so, listing them as "security guards", besides that, they will get chased by the police and if hit while in chase, Tommy will be given the "Good Citizen Bonus" of 50$.
During the stroyline, they are not as important nor powerfull as the other gangs, mainly because they are a legal security group, but they do make some appearances in the storyline, protecting Alex Shrub, Love Fist and a counterfeiting protection bussiness for the Vice City Triads, their most important appearence is when they try to move in in Tommy's protection rackets in Ocean Beach, for which Tommy kills the guards involved adn destroys the local PIG office.
They roam around unlike any gang, since they patrol the streets individually, shoot at Sharks members at the mall and Vercetti Gang members if near Vercetti Estate and will only shoot Tommy in self-defense or if Tommy shoots anywhere.
Sharks
Also called Streetwannabes, the Sharks are a band of thugs who roam around the North Point Mall and Prawn Island, their leader, who was unnamed, steals from Ricardo Diaz and gets killed by Tommy in an airstrike, leaving the Sharks with no known leader.
Similarly to the PIG, they are not as important nor powerfull as the other gangs, but they are even less relevant than the PIG in the storyline, only appearing a few times, and in all of the missions that they appear in, they get killed by Tommy.
They seem to be on bad terms with the Vice City Bikers because they stole Mitch Baker's motorcycle and Diaz' Gang before they disappeared, because the leader of the Sharks stole from Ricardo, they also got ambushed by Tommy in orders of Umberto Robina, but they are not necesarilly enemis of the Cubans.
They are not hostile even after killing their leader and will only shoot in self defense or if hijacked, they will always shoot against the PIG's guards when one enters the mall.