"How many languages do you speak?"
...is not, contrary to popular opinion, the most appropriate response to "I'm a linguist." That's because linguistics is not the study of learning as many languages as you can (although that may be involved), and because linguists know that it's difficult to define when you really know a language. As my friend Andrea Jones Berasaluce once said (approximately) "Learning a language, if you're really motivated, takes maybe six weeks. Knowing a language takes a lifetime, and you're still not done."
But since you asked, here's my linguistic profile:
I was raised monolingual in a pretty standard version of American English. I pronounce pin and pen differently, tire and tar differently, and caught and cot almost exactly the same. My paternal grandmother speaks English and Spanish natively, and my paternal grandfather spoke English, Spanish, and Sicilian natively. They taught me a little Spanish.
In eighth grade, I took a Latin class. When I realized that I could actually learn a foreign language, I started teaching myself Italian.
In high school I took Spanish through the AP classes. On my own, I worked on Italian and French, and eventually German.
I took one Spanish course in college, and the equivalent of 2 years of German. I minored in French and spent a semester at a university in Paris. I also took a class on Old English.
If I ever get back to learning new languages, Russian, Korean, and Swahili are next on my list. I also think it would be fun to study a creole and a sign language.