Team Rocket
Team Rocket (Japanese: ロケット団) is a highly organized criminal syndicate "in pursuit of evil" headed by Giovanni (called "The Boss" by his underlings) and based in Kanto. Its main focus is in stealing or capturing, then selling, rare and/or strong Pokémon, but it also conducts cruel experimental research on Pokémon. Its final goal is to take over the world using Pokémon.
In the games
In Kanto
In the Generation I games, and Pokémon FireRed and LeafGreen, Team Rocket focused its attention on Kanto, distributing Pokémon using the Rocket Game Corner in Celadon City and its secret hideout underneath. It also committed various crimes including breaking into a house in Cerulean City, killing a Marowak in Lavender Town, and taking over Saffron City and the Silph Company Headquarters for its products, including the Master Ball. However, the games' hero/heroine ousted the team out of its hideout underneath the Game Corner, out of the Silph Company Headquarters, and out of the Pokémon Tower, defeating Giovanni in a Pokémon battle twice. However, Giovanni returned to the Viridian City Gym, as he was also the legitimate Gym Leader there, but the hero/heroine defeated him there, too. Then, Giovanni, acknoledging him/her as the better trainer, disappeared without a trace.
Three years later, Team Rocket returned to Kanto to steal a critical part from the Power Plant, but this plot was on a small scale and was ultimately the last appearance of Team Rocket in the games. Since only one member was involved, which is rather unlike most of Team Rocket's plots, it is possible that this was a semi-independent member that did not hear of Giovanni's fall.
In the Sevii Islands
In FireRed and LeafGreen, Team Rocket had a branch in the Sevii Islands, searching for the Ruby and Sapphire gems. This branch was based in the Rocket Warehouse in Five Isle Meadow in Chrono Island. In the end, the games' hero/heroine defeated the Admin there, making him realize that with Giovanni defeated in Kanto, all is lost for the Sevii branch. The team subsequently pulled out of the Sevii Islands. It has not been seen there since.
In Johto
In the Generation II games, three years after the aforementioned events, Team Rocket focused its attention on Johto, setting up another base underneath a shop in Mahogany Town and building a machine that emitted high-frequency sound waves, enraging the Gyarados in the Lake of Rage north of Mahogany Town. With the help of Lance, the League Champion from Indigo Plateau, the games' hero/heroine foiled the team's operations. In a final and desperate attempt to contact their former leader, Giovanni, members of the team attacked the Radio Tower in Goldenrod City, but were ousted by the hero/heroine yet again.
In the anime
In the anime, Team Rocket is based in Kanto, with many smaller branches reaching out in Kanto and Johto. Giovanni is the Gym Leader of Viridian City. There is also an underground school for training aspiring Team Rocket members. In addition, Team Rocket had its headquarters near Pallet Town and Viridian City, but this was destroyed by Mewtwo in its rage; it is unknown where the headquarters are now.
A trio of members, Jessie, James, and a talking Meowth, were defeated when on assignment by Ash Ketchum, and since then have been following him everywhere on his journey, attempting to steal the Pikachu that defeated them and any other Pokémon, items, and money that happen to appear on the way. They are currently deluded into thinking that they have been sent by Giovanni to establish a new branch of Team Rocket in Hoenn, and Meowth often fantasizes about pleasing "The Boss" with some hairbrained scheme- while replacing his Persian as his new favorite pet. In Giovanni's opinion, however, they are "a bumbling trio" that "can't do anything right," and as of yet, they have failed to come up with a single thing to present to him while eating up the organization's funding with their many robots and schemes. Occasionally, the trio is also forced to work with Ash and company in certain extreme circumstances.
Other notable members of Team Rocket include Butch, Cassidy, Dr. Shiranui, Attila, Hun, Namba, Tyson, and Vicious. Jessie's mother, Miyamoto, was once a member before she disappeared on an expedition to capture Mew while serving under Giovanni's mother, On'na Boss.
Team Rocket has attempted to do many major and potentially globally-altering operations, including cloning DNA of Mew and altering it to form Mewtwo. This stemmed out of a desire of Giovanni to appease his mother's obsession with Mew. When Mewtwo finally finished developing, he deceived Mewtwo into working for him, including defeating Gary, but in the end, Mewtwo destroyed the secret Rocket headquarters and attempted to take over the world as revenge for his unnatural creation. Team Rocket also attempted to capture and control a Lugia and Celebi, and it also created a device that could force Pokémon to evolve.