StarCraft/Beginnings

Xel-Naga's Creations: Protoss and Zerg
The Xel'Naga, an ancient spacefaring race obsessed with breeding the ultimate race, found hope on Aiur, where they civilized the psionically attuned Protoss based on their purity of form. After the creators revealed themselves and built a temple, however, the Protoss fell into disarray. The Xel'Naga left in defeat, and never learned that the Protoss had reunited under the Khala (the Way) and had later formed two subgroups, the High and the Fallen (Dark) Templar. The Xel'Naga realized that the cause of the Protoss rebellion lay in their independent minds. Though they marked their arrival on Char and Braxis with more temples, but only when they arrived on Zerus did they finally find their target, which exhibited purity of essence. They created an Overmind and minion Cerebrates to control their new race, the Zerg, with each Cerebrate controlling a Brood. The Zerg evolved into fierce community covering multiple genuses. With its psionic powers, the Overmind lured a herd of space creatures to the planet. With the genetic code of the Behemoths (Overlords), the Zerg became free of their terrestrial confines and the Overmind launched a surprise attack against the Xel'Naga, who were never heard of again. At the beginning of the StarCraft saga, the Protoss populated Aiur, Braxis, and Shakuras, while the Zerg had shifted its Broods from Zerus to Char to direct its long-awaited campaign of overcoming the Protoss.

Caught in the Middle: Terran
The Terrans in StarCraft are outcasts from Earth, which has been taken over by the United Powers League. The original Terran colonists were sent aboard giant ships to travel far into deep space. One of the colonies, Tarsonis, forms the Confederacy, an interplanetary empire over the Koprulu Sector. At the beginning of the game, the Terrans have claimed 13 worlds. The Confederacy's kleptocracy and oligarchy has angered many of its subjects, and some groups, such as the Sons of Korhal and Raynor's Raiders, have begun to demand greater liberty. When the rebels on Korhal proved victorious, the Confederacy annihilated and glassed the planet's surface with nukes. All life on the surface was extinguished. However, as Episode 1 shows, the Confederacy's grip over its realms continues to collapse. For the rest of the storyline, you will have to play the game.

The Continuation of the Saga: BroodWar
Wikipedia has more on this subject.

Blizzard now mysteriously Warps In the planet of Earth and its United Earth Directorate, along with the UED Expeditionary Force which begins its invasion of Koprulu, Aiur, Braxis, and Char in Episode 5. Meanwhile, the Protoss battle the Zerg on Shakuras and fulfill a Xel'Naga legacy, while the Zerg are torn between the Queen of Blades, UED Scientists' Psi Disruptor, and Daggoth's Overmind Cocoon. BroodWar continues the StarCraft saga with the intrigues of the Protoss, the invasions of the Terran, and the infestations of the Zerg. For the rest of the storyline, you will have to play the game.