According to an interview with distinguished cognitive neuroscientist Ellen Bialystok, bilingualism has various benefits for the mind, including delayed onset of Alzheimer symptoms. Bialystok, who has been studying bilingualism for nearly forty years and now uses neuroimaging in her research, maintains that being bilingual "rewires" the mind and makes it more supple and efficient, at least in some ways. However, she means "bilingual" in the real sense of the word- using two languages with near-equal facility on a regular basis. She does not include people who just know a second language.
My own experience with bilingualism has been positive and enriching. I learned Italian at the age of seven, after no previous exposure to it, when my parents moved to Italy and placed me in a local Catholic school. There were no special classes for me, but I'm sure the nuns must have given me special attention in the first months. My little friend Anna Maria, who lived next door, also served as a patient unpaid tutor.
I don't know if there is a direct causal relation, but I have since taken a shine to all things linguistic and literary, reaching the unusual position for an American of knowing five languages. I am intrepid in both English spelling and ancient Greek grammar. I am perhaps the only foreigner in the world whose French has not been scorned by the French. And I am showing no signs of Alzheimer's. On this basis, I can heartily enjoin you to take up or keep up with a foreign language (hint: try Italian) and encourage your young 'uns to perfect another language from an early age.
The video shows a slightly less scholarly (but more entertaining) take on language and bilingualism by comedian Eddie Izzard.