Learning a foreign language at any level is helpful. First and most broadly, it helps to understand other cultures and other people, and helps talking with people sometimes. Then there are the cogntive benefits of keeping separate languages straight in your head and being able to think in another language than one's primary language. In my own experience, I never did serious study of any foreign languages until college, and I knew by then I was unlikely to become fluent in any one. But I got conversational abilities in three, and learned to read those and three more, and osmtimes for fun, I pick up language grammars and work through them. Sometimes I run into people who know one of these and it helps as a conversation starter. It has opened doors, too: I had a desk job at the library in grad school, and was recruited into foreign language cataloging. Overall, though, the best reason is probably the first one: to understand the world around us and the other people who inhabit it.
The famous poet-philosopher Wolfgang Johann von Goethe once said, "He who does not know another language, does not know his own."
Studying a foreign langugage forces one to come to grips with the structure of one's own language since there must be something to which one can relate the learning of the new language. Of course, if one speaks English and studies Latin or Greek, for instance, the student learns the roots of many English words. With the Norman Conquest of 1066 effecting French as the official language and the written language of early literature in England, a study of French provides the English speaker with insights into both grammar and vocabulary and structure.
The study of any foreign language helps a student to step "outside the box" of one's own culture and learn, not only of another culture, but also perceive all it means to be of one's own culture. For, language is culture. To quote Goethe again,"Learning another language is to acquire another soul."
According to Thomas Friedman, an writer who writes about economics for the New York Times, The World is Flat. The global economic picture of the future ties all countries and all cultures closer together than ever before, and while English tends to be language that binds the world (there are way more English as a 2nd language speakers than there are people who speak it natively) it is going to be more important to speak other languages as the world's economy becomes more and more interdependent.
From a strictly financial point of view, learning a second (or third) language can be quite profitable when you go looking for employment. I live in Florida, and speaking Spanish is required for many jobs. People who speak both English and fluent Arabic languages are in great demand these days, particularly in government and federal agencies.
#3 makes an excellent point; if you are cloistered in your own first language, you will miss nuances that trip people up. If you learn a different language you can see how language and meaning changes by context, gesture, and sentence structure.
Check out this website. The author is an Irish man who goes to different countries and learns their languages by listening and conversing. It's very interesting stuff.
There are benefits to learning a lanaguage even if you don't become fluent. First of all, you develop a better understanding of your own language's grammar and syntax from learning a new language. Second of all, you can also learn new things about another culture and appreciate differences.
In a sense, it is not unless you learn them really well. (I say this as someone who is fluent in one foreign language and conversant in two more -- so I'm not just some bigoted American who thinks that other languages are beneath me).
To me, the most important thing about other languages is that they give you a better understanding of other cultures. Understanding other cultures actually is important because it helps us not be too arrogant or set in our ways. It helps us understand that there are other ways that might be as valid as our own. When you truly know a language (and can listen to music in that language or watch TV in it) you get to understand the other culture better and that truly is important.