Most Koreans are more concerned with finding a job with stability rather than following one's passion and building a career based on that. There are two main career paths that offer this kind of stability. The first is what is called a jeong-gyu-jig (정규직) position at a major company. Jeong-gyu-jig is a type of employment in which your employment is more-or-less guaranteed until retirement barring some major violation of company policy. The second one is employment as a public servant, which in Korea is referred to as an "iron rice bowl" because it provides such stability. In both these cases, people will of course generally end up doing work related to their education background, but at the same time they tend not to have a lot of say in exactly what position they end up in.
According to a 2014 survey conducted by one of the major Korean job search sites the most popular employers among university students are as follows.