Team Rocket - "While its main focus is stealing or capturing rare and strong Pokémon, and subsequently selling them, it also funds and conducts cruel experimental research on Pokémon." They basically steal strong and rare Pokemon to sell them. (they also moonlight as scientists)
Team Magma - Expanding the earth for...reasons? real estate maybe?
Team Aqua - Expanding the Oceans for...reasons? they like fish maybe?
Team Galactic - "Their goal is not limited to the Pokémon world, but is the recreation of the entire Pokémon universe." they want to recreate the universe.
Team Plasma (BW) - "Team Plasma's ultimate goal is to "liberate" all Pokémon from their trainers, by either convincing the trainer to release their Pokémon, or by theft." they think Pokemon are unhappy with their trainers and want to liberate them.
Team Plasama (BW2) - 2 years after the events of BW, this time they just want to take over the Unova region...
Team Flare - "Their goal is to create a "beautiful and better" world while making money, eliminating everyone who do not follow their standards." They want to make the world beautiful and make money while doing so.
Team Skull - Team Skull is composed of misfits who failed the island challenge. They run around the Alola region causing havoc, stealing Pokemon and bus stop signs (?). Unlike other teams from previous regions, they don't have a specific goal. "Some men just want to watch the world burn".
Sources - Bulbapedia and playing every Pokemon game.