The five main reasons (that I have encountered) are:
Students learn Japanese because they work for Japanese companies or their business counterparts are Japanese.
Students who go to Japan on business trips (shucho), or who meet Japanese colleagues in the course of their work, are some of the luckiest because they can try out their linguistic skills with native speakers.
They are also lucky because their companies usually pay for their lessons.
To gain a qualification
Some people need a concrete goal if they are going to study something so they decide to do a course that will give them a certificate at the end and/or so they can add something to their CV.
One of the most popular qualifications is the yearly (in December) Japan Foundation exam (Grade 4, the lowest, to Grade 1, the highest).
JETRO’s Business Japanese exam is also popular with pre-/advanced learners, particularly those who have lived in Japan for some years.
Some students prefer to sit the GCSE, or the A-level exam. The A level is popular with people who are around the grade 2 level of the Japan Foundation exam.
The LTI (Language Testing International)’s OPI (oral proficiency interview) is an exam for those who would like to study for an MBA in an American university. However, this examines only your oral communication skills through a phone call from New York for 15 minutes, and you must be graded at least as ‘Advanced Low’ to be accepted on an MBA.
Some learn Japanese because one of their parents, most likely the mother, is Japanese.
Due to a variety of reasons, their linguistic skills have not been fully developed: for example, one student was capable of talking about current issues, but was not able to write/read.
Others can communicate on daily matters, but start showing some strain when the conversation goes beyond that.
A boy, aged 19, decided to take lessons because he is embarrassed not being able to communicate in Japanese.
One female adult student wanted to talk more intelligently because she thinks that is what she is expected to do.
Such students usually progress quickly because they have (subconsciously) embodied the structure of the language while listening to Japanese people talk.
Learning for pleasure is also a good reason to learn Japanese.
Some students like the challenge of learning a foreign language and choose Japanese because they have already familiarized themselves with European languages such as French, Spanish or German, and they would like to study something completely different.
Some have Japanese girlfriends or boyfriends, who have volunteered to teach them.
The downside of this is that men learn women’s Japanese. Other students like travelling and want to visit Japan.
Often they are intrigued by the famously orderly and polite Japanese society, and this motivates their study. Some students like Japanese food so they frequent Japanese restaurants where chefs kindly teach food-related words. This then encourages them to learn more about the language.
To develop what they have already learnt
School-age students sometimes choose to study Japanese because they learnt some at school and do not want to forget it, or because their parents worked in Japan and they learnt some while living there.
Chinese students often find Japanese fairly easy, because they know how to write the kanji.