I can think of 3 reasons. The first one is the way it sounds. It's smooth, composed and sometimes chirpy. I like how onomatopoeias are widely used in this language. It's like Japanese people speak with "sound effects" ;)
The second reason is its rich writing system. It has everything you could ask for; a cute and soft-looking alphabet (Hiragana), a bold, impressive one (Katakana), and a scary one (Kanji!... I'm kidding!). Despite being one of the biggest challenges for students of the language, the idea behind these last characters is truly fascinating. And it also makes of Japanese a very visual language. For example, just a quick glance at a kanji can give you a general idea of a subject...
The last reason is the cultural differences expressed in the language. How could I explain this?... Those things that usually get "lost in translation": the different levels of politeness, honorifics, differences in language usage between the sexes (masculine and feminine ways of speaking), less use of pronouns and the preference for speaking in third person, just to mention a few.
All of this makes it a beautiful and interesting language to me!
thank you very much!