Those who know many languages live as much lives as the languages they know

-Czech popular saying

=)

I consider there will be more than 100 answers to the question if you ask 100 people in different times. Linguistic specialists would prefer to conclude these into "motivation" and it can be classified into 2 groups : intrinsic and extrinsic motivations. 

In terms of myself,  to learn a new language is a good way to look through the window to see another world. 

I HAVE TO learn English, because I work in an international company, and all files are in English. During the work, my poor English trouble me so much. Especial the written English. This is the original motivation of my English learning.

But somethings changed after I was into English learning. It is a total different culture beneath the English language. So I have read some history books of America by native writers. So far, English learning is my habit, the learning process give me more interesting other than boring.  

I started learning French and Italian in school and want to finally become fluent in those languages, perhaps work with them in the future (I'm a translator). So I suppose you could say that my motivation is both professional and personal ambition.

I want to learn other languages later as well, once I'm "done" with Italian and French, for example Japanese, Croatian, Greek and Vietnamese. I want to learn them because I want to travel to countries where those languages are spoken.