"So, how many languages do you speak?"
If you tell someone you have a linguistics degree, there is something like a 90% chance they will ask you this question.
Hearing it always puts me briefly at a loss. For one thing, it's a bit ambiguous. Do you want to know how many languages I'm fluent in? Which ones I've studied? How many I can carry on a conversation in? This leads to a rather bloated answer of "Well, the only language I'm really fluent in is English. But I've studied French, Mandarin, Finnish, Japanese, and American Sign Language. I don't really remember any Mandarin or Finnish, though. I'm probably most comfortable conversing in ASL, but I can read a bit more French and I can understand a lot of Japanese. I can speak a few words of Korean, Hungarian, Swahili, German, and Spanish. But then again, who doesn't know a few words in Spanish!" In case you couldn't tell, my breadth of foreign language is much greater than my depth -- I love to start learning new ones, but I abandon them shortly. I consider myself monolingual, though I really would like to someday be fluent in ASL and Japanese.
But the bigger issue with that question of how many languages I speak is that linguistics isn't about the study of foreign languages. Linguistics is the science of language, and a linguist is someone who studies language itself. Of course, to get a decent understanding of language, it helps to be familiar with a few of them, hence why most undergraduate programs require foreign language classes. (My school, the University of Washington, required a year each of two.)
The field of linguistics can divided between formal (or theoretical) linguistics, and applied linguistics. Formal linguistics looks at the stuff languages are made of: phonetics (speech sounds; anatomy and acoustics), phonology (how those sounds are combined in real languages), morphology (how words are formed, e.g., roots and affixes), syntax (how sentences are formed), and semantics (meaning). Applied linguistics is, well, everything else about language, such as sociolinguistics (the social/cultural aspects of of language), psycholinguistics (the psychology of language), historical linguistics (origins of language and how they change over time; etymology), and computational linguistics (natural language meets computer science -- I'm not clear on a lot of the details of this field).
UW requires linguistics majors to take an intro class, phonetics, phonology, two levels of syntax, and either morphology or semantics, plus several electives in applied linguistics. Personally, my biggest interests are psycholinguistics, phonetics, and sociolinguistics. Syntax and morphology bored me to tears.
Much as I love learning foreign languages, my biggest love is my mother tongue, English. English phonology is probably my strongest area of linguistic knowledge. I especially love studying the differences between accents. Despite the boredom of my syntax classes, I love to analyze the structure of sentences I or other people speak. And I love to dig into the meanings of words... just ask my friends how often I call for "LANGUAGE SURVEY TIME." ("Do you read a difference in meaning between 'bravery' and 'courage'?") Psycholinguistics is the other area that I love as much as or even more than English linguistics. It was easily the most fascinating and fun class I ever took at college. It covers how the brain processes language, how children acquire it, language disorders, the evolution of language in humans, etc.
The other question I get a lot, since I'm young and haven't settled into a career yet, is what I plan to do with my degree. And my answer, in so many words, is "Nothing." Unless you are fluent in more than one language, an undergraduate linguistics degree doesn't qualify you for much. I don't have much desire to go to graduate school at this time, and I'm not very interested in computational linguistics, which is big in this area since Microsoft is here. I wanted to go to college for the sake of learning about things that interest me -- which I did, along with gaining the tools I needed to keep studying independently. I wanted a BA specifically because it looks good on a resume and qualifies you for more jobs, period. My work doesn't involve linguistics now, and there's a chance it never will. But I do very much love studying it.
For my fellow linguistics geeks who are wondering what my other electives were: linguistic typology (which I didn't care for at the time, but it ended up being extremely useful for conlanging), Structure of ASL, Second-Language Acquisition (theory, not pedagogy). I also was a research assistant for one quarter in a neuroscience lab, where I had the only-fun-if-you're-nerdy task of transcribing tapes of small children speaking.
