Why Did Kerrigan Become Zerg in StarCraft?

Sarah Kerrigan became zerg because Arcturus Mengsk abandoned her to the Swarm on Tarsonis, and the Overmind chose to infest her instead of killing her. It wanted her psychic power, and StarCraft II later reveals it hoped she could free the zerg from Amon. Years later she chose to become zerg again on Zerus, to get the strength to kill Mengsk. (StarCraft; StarCraft II: Wings of Liberty; StarCraft II: Heart of the Swarm)

The betrayal on Tarsonis#

In the original StarCraft, Kerrigan is a ghost, a telepathic agent, and second-in-command of Mengsk's rebel Sons of Korhal. Mengsk's war against the Confederacy reaches its capital, Tarsonis, where his forces plant psi emitters that draw the zerg onto the planet. Kerrigan and Jim Raynor are both uneasy. She had already planted one of the devices under protest, telling Mengsk she didn't think anyone deserved to have the zerg unleashed on them. (StarCraft)

When the protoss arrive and start fighting the zerg on the ground, Mengsk worries they'll give the Confederates time to escape. He sends Kerrigan to hold them off and protect the zerg. Raynor wants to go with her. She tells him she'll be fine. (StarCraft)

She beats the protoss, but a wave of zerg rolls over her position. Mengsk orders the fleet to pull out. Raynor is horrified, and when Mengsk won't go back for her, Raynor and his men break away from the Sons of Korhal. That's the end of the terran campaign, and the start of Raynor's Raiders. (StarCraft)

The game never has Mengsk spell out his motives in full. What it shows is that he left her when he could have tried to save her, and Kerrigan never forgets it. In Brood War she tells him he practically fed her to the zerg and blames him for everything she's been through. (StarCraft; StarCraft: Brood War)

What the Overmind did with her#

The zerg campaign picks up from there. The Swarm captures Kerrigan instead of killing her, and the Overmind has her sealed in a chrysalis and carried to Char. While she's inside, her telepathy reaches out to Raynor and Mengsk. When she emerges, she calls herself the Queen of Blades, drives off Raynor's rescue attempt and lets him go. (StarCraft)

The Overmind is clear about its first reason. It sensed her psychic power and saw a weapon against the protoss. When the cerebrate Zasz complains about her wilfulness, the Overmind tells it her nature is just as intended. Kerrigan soon goes after Confederate ghost files to break the conditioning that still held her powers back, and grows stronger fast. (StarCraft)

The real reason, revealed later#

Wings of Liberty changes the picture. In the mission Echoes of the Future, Zeratul touches the dead Overmind's memories on Aiur and learns that the Overmind had been made a slave. The fallen xel'naga Amon had forced it to destroy the protoss as part of a plan to wipe out all life. The Overmind couldn't fight that order itself. It made Kerrigan in the hope that she would one day free the Swarm, and the vision shows a future where Amon wins once she is dead. (StarCraft II: Wings of Liberty)

So Kerrigan's infestation was, in a sense, deliberate on two levels. Mengsk wanted her gone, and the Overmind wanted her specifically. The second point is the twist that drives all of StarCraft II and ends with her becoming a xel'naga. (StarCraft II: Wings of Liberty; StarCraft II: Legacy of the Void)

The second time: a choice#

At the end of Wings of Liberty, an ancient xel'naga device turns Kerrigan mostly human again. That story is on how Kerrigan became human again. (StarCraft II: Wings of Liberty)

In Heart of the Swarm she goes back to the zerg on purpose. After the Dominion attacks her refuge, she's separated from Raynor, and a news broadcast claims he's been executed. With nothing left but revenge, she takes command of the Swarm again. On Zerus, the zerg homeworld, the ancient zerg Zurvan tells her she must let the planet remake her if she wants the power of the primal zerg. She knows it will cost her humanity and agrees anyway. She enters the first spawning pool, seals herself in a chrysalis and emerges as the Primal Queen of Blades, hoping Amon will have no hold on her this time. (StarCraft II: Heart of the Swarm)

That's the difference between the two times, if you want it in a line: the first was done to her, the second she did herself. When Raynor sees her again, he's horrified that she'd do it willingly. (StarCraft II: Heart of the Swarm)

Read more in the full Sarah Kerrigan biography and StarCraft story explained. (StarCraft; StarCraft II: Heart of the Swarm)