Evangeline Lilly, Kate on LOST, didn’t plan on becoming an actress. In fact, she just stumbled into it while she was studying international relations. She was approached by someone from the Ford modeling agency, literally on the street, to become a model, but she turned it down at the time. Later, when she wanted to earn some extra cash, she went to the Ford agency and signed up as an actress. She played bit parts in various commercials, movies and television shows until she landed on the island with LOST.
You can read more about how Evangline Lilly became an actress in an article by Wanda Lebowitz over at Associated Content.