People ask me this question all the time, and I never really know how to answer. I can't give the answer most seem to expect, as I've never really had an interest in anime, manga, or Japanese literature or movies (except for a recent interest in Miyazaki's work). I've always been interested in learning another language, but I took 2 years of Spanish in high school, never acquired an actual passion for learning it, and promptly forgot nearly everything immediately after graduating. I had a free class slot free my sophomore year in college, so I figured I'd try again. I had never had more interest in Japan or Japanese than the average American, but my university offered it so I took it. I studied for about 8 months without really getting that all important passion for learning before I agreed to volunteer in a program at my university where Japanese students study English for five months, staying in the dorms on campus. I quickly became good friends with many of the students, and my desire to learn just kept growing from there, culminating with my 3 month language study abroad program I took this summer.
My reasons for studying now... There are several. I feel like accomplishing something as huge as becoming fluent in Japanese would make me more confident in myself and make me a better person in general. After staying in a completely different culture for several months, my mind has been opened up so much; it really gives you a better perspective of the world. I think a summer abroad should be a highly recommended, if not required thing for students.
I used to love the idea of kanji, but I abhorred trying to study it, until I found RTK. I'm only about 350 characters in, but I'm still going more or less strong, and it really has made me see what a beautiful and fascinating system it is. I was so surprised to find myself actually enjoying studying kanji for the first time.
Then there are the selfish reasons.

I enjoy seeing the amazed looks on people's faces when I can read some Japanese text, or translate some words. I don't want to be the typical monolingual American. I get a sense of fulfillment seeing my progress at something many people believe is impossible or at least extremely difficult. The girls... I see more as a perk than a reason.
Something interesting I have noticed... While taking the 2 years of Japanese offered at my university, and even while taking Japanese language courses in Japan, I never really studied beyond what coursework was given in the class. Since returning from Japan, however, I realized that I would have to start doing self study if I didn't want to forget everything I had spent so much time acquiring. Since realizing that, I have been studying WAY more than I ever did while I was actually enrolled in courses. It doesn't even compare. Has anyone else had a similar situation?