A Fleet (船団,Sendan?) or Armada (艦隊,Kantai?) is a seafaring organization that is strong or large enough to facilitate a large number of ships to support the main transportation of said organization. Not many organizations have the funds or influence to support one, but if one is able to, they can exert a lot of influence across the Blue Sea.
A fleet, unlike a normal alliance has a hierarchy, with one clear leader, with all the other ships' captains being subservient to them. The Marines are shown to have a very strict hierarchy, assigning ranks to each sailor, thus facilitating a chain of command, in the event the upper ranks are isolated or eliminated in battle.
Pirates, however, are much more laid back. If it's a single crew fleet, the most powerful and highest ranking combatants are generally put in charge of their own division (or ship); as such they follow the orders of the fleet admiral (or "commodore" in the English dub) full time. With a multi-crew fleet, the subordinate crews form a "parent-child alliance" with a single "parent" and his crew ranking above the "children" crews. The captains of each crew are effectively division commanders in their own right. However in a multi-crew fleet, unless the fleet's leader orders it, the individual "children" crews are permitted to roam freely and act as they please, provided their actions don't hurt the "parent's" or "sibling's" crews.
In the world of One Piece, if a fleet belongs to a country but is independent of the Marines and the World Government, they are generally labelled as a Navy (水軍,Suigun?). They are technically not considered pirates, and thus not illegal (as Sai's presence was allowed at Mary Geoise during the Reverie) but at the same time are not a part of and do not possess the universal authority of the Marines, and as such, may come into conflict with them.
A specialized fleet of the Marines, consisting of 10 warships under the command of 5 vice admirals. It is considered to be the Marines' ultimate military action, falling under their doctrine of "Absolute Justice". The 10 battleship lays waste to the target location mercilessly, utterly disregarding any civilians and comrades, and are willing to even to sink any of their own ships if necessary. Only those ranking of Admiral or higher may initiate the Buster Call, as well as grant those lower ranking the permission. Once the Golden Den Den Mushi is activated, 5 available vice admirals and 10 ships are gathered, and the summon cannot be rescinded.
They were once one of the strongest forces in the East Blue, with 50 ships and 5,000 pirates to their name. However, they lost all their ships shortly after entering the Grand Line to the hands of ShichibukaiDracule Mihawk. It is unknown what has become of them after Monkey D. Luffy defeated their captain.
This organization, which was once comprised of over 2,000 men and several ships, mainly dealt in bounty hunting and Underworld trading. The ultimate goal of Baroque Works was to be resolved in Operation Utopia, however several of their ships were destroyed by Portgas D. Ace, while the rest (after Crocodile's defeat) were captured by the Marines.
Originally a small crew of only 10 or so members, shortly after the Battle of Marineford they swiftly took over the majority of Whitebeards territory, with Teach ascending to the ranks of Yonko. Now ruling over several islands, they have blossomed into a full fledged fleet capable of supervising them. Though the full size of the Blackbeard Pirates is unknown, they have at least ten ships to their name, with their division commanders are known as the Ten Titanic Captains (10人の巨漢船長,Jū-nin no Kyokan Senchō?).
A large fleet in its own right, it has 8 ships and 1,000 members, it has been active long before the current storyline, with the former head, Don Chinjao, once being a rival to the hero Monkey D. Garp. This group appears to be based in the Kano Country, and have for generations been led by the Chinjao Family. They joined the Straw Hat Grand Fleet after their leaders were saved from enslavement as toys at the hands of the Donquixote Pirates.
A massive fleet commanded by Orlumbus, comprised of 56 ships and 4,300 members. In a similar manner as the Happo Navy, Orlumbus too was turned into a toy and was doomed to a life of enslavement, but was saved by the Straw Hats. Due to this incident, he swore himself and his fleet to Monkey D. Luffy.
The Neo Marines were a non-canon radical organization led by the former Marine Admiral, Z, and was made up of a large fleet of ships. The ultimate goal of the Neo Marines was to be resolved with their plan, the Grand Reboot, however, in the end, it was thwarted by the Straw Hats. It is unknown what became of them after their defeat at the hands of the Straw Hat Pirates, and their leaders death at the hands of the Marines. They were the main antagonists of One Piece Film: Z.
A large fleet comprised of dozens of ships, each shaped like a large Den Den Mushi. The fleet is unique, serving hybrid functions. It is used to transport the Germa Kingdom's army, Germa 66, in both its official national engagements and in its Underworld mercenary activities. When all the ships are assembled and their "shells" interlocked, they also form the "territory" of the ocean-going Germa Kingdom itself.
The Big Mom Pirates are in control of a massive fleet comprised of numerous flagships, as well many Tarte ships used as guard posts and scouts for their territories within Totto Land. Their fleet formerly included both the Fire Tank Pirates and Sun Pirates before they disassociated themselves from Linlin and her pirate crew. There were plans to acquire and incorporate Germa 66's fleet along with their scientific knowledge through what was ostensibly a political marriage to form an alliance between the Vinsmoke and Charlotte Families, but was in reality a plot by Linlin and her crew to assassinate the Vinsmokes and gain everything for herself. After their plot was foiled and revealed to all at the Tea Party, the alliance between the families is no longer active, preventing the addition to their fleet.
Known twenty-three years ago as one of the world's biggest pirate fleets, they attempted a bold plan of world domination, using the Ancient Weapons. However, after Gol D. Roger (who was the only one who knew the locations of said weapons) refused to join them, the fleet clashed against the Roger Pirates, in what is later known as the Battle of Edd War, and lost, incurring heavy damage. Shiki was later imprisoned after storming Marineford due to Roger's surrender, but later escaped. In One Piece Film: Strong World, Shiki gathered his fleet together again in order to act out his new plan of world domination; by using giant mutated animals to conquer his enemies, starting with the East Blue. However, after the fleet was defeated by the Straw Hat Pirates, they were then captured by the Marines. Though the full size of the fleet was never confirmed, in an anime filler arc, a certain crew was offered the position of 51st division in Shiki's fleet should he successfully complete a certain mission, suggesting that Golden Lion Pirates fleet had at least 50 other divisions.
The Whitebeard Pirates were once a crew led by the Yonko, Edward Newgate, whose influence guarded and supervised several islands throughout the New World. The crew by itself has a large fleet comprised of 16 divisions, with over 1,600 crew members, but it is further reinforced by 43 allies, all seasoned veterans in the New World. This fleet made its appearance in the Battle of Marineford in the Marineford Arc. After losing their captain, it seems that the 'parent' crew have gone into hiding, while most of the 'children' crew are still active. However, 16 'children' crews are noted to have been defeated and captured by the Shichibukai Edward Weevil, leaving at most 27 crews still active.
The Straw Hat Grand Fleet was formed at the end of Dressrosa Arc, comprised of seven divisions: the Beautiful Pirates, the Barto Club, the Happo Navy, the Ideo Pirates, the Tonta Corps, the reborn Giant Warrior Pirates and the Yonta Maria Grand Fleet. An unusual fleet, Luffy initially turned down their offer for the alliance, as he finds such things as bothersome. After Luffy conveys to them that his ideal of Pirate King is not to be important, but to be free, the leaders were touched by this and decided to exercise their own free wills. They vowed themselves to be his underlings, without the Straw Hat captain having to be obligated to respond in turn.