In short: yes! I think there is no reason not to learn a second language if you have the chance/interest to do it. School is obviously a good time for it, but there really is no age limit or requirements to start learning!
Obviously as a language teacher I am quite biased, but I can tell that the fact that I can speak two languages fluently, jabber one well enough to survive, read two and understand some things in two more, gives me the amazing chance to see things differently.
This is the opposite of Orwell's novlang, supposed to prevent "bad" thoughts by simply removing the words for it. A new language will actually add new words, grammar structures, that will enable you to think new things. How exciting is that?!
Any language can, and will!, give you the chance to learn new concepts, new ideas, that simply never occurred to you because you didn't have the words for them. A different grammar will also allow you to put things in a different perspective.
There is nothing like learning a new word, in a new language or in your own!
