In MK Trilogy Rain's storyline is: Born in Kitana's former world of Edenia, Rain was smuggled away from the realm as a small child shortly after Shao Kahn's takeover. Thousands of years later he resurfaced, his allegiance belonging to Kahn. He chose to betray his homeland rather than suffer at the hands of Kahn's extermination squad.
And his ending is:
Rain fights valiantly for the emperor Shao Kahn. But it would be Kahn's own step-daughter, the princess Kitana, who turns Rain against him. Like Kitana, Rain's origins also come from their former realm of Edenia. He learns that his father was once a general in Edenia's army and died at the hands of Shao Kahn himself. Enraged at the truth about his history, he joins Kitana in allying with the Earth realm warriors. But his allegience comes under question when he mysteriously disappears during an extermination squad attack. to prove his loyalty he embarked on a suicide mission to destroy Shao Kahn and end the menace once and for all.

Here is the OLD version of Rain's storyline that made it into some instruction booklets by mistake. Keep in mind this is not his true storyline:

Rain is an assassin working freelance. He was once a member of the Lin Kuei along with Sub-Zero, but left the clan under mysterious circumstances. Years later, Rain is found working for Shao Kahn as an assassin in the Outworld. Born a human, he finds himself questioning his loyalty towards Kahn after watching the invasion of Earth.