In D&D, and to be honest every RPG game I've played where I can remember the rules for languages, it comes down to a binary distinction regarding languages. You either know the language, or you don't.
Of course, as a language teacher and language student, this it completely unrealistic. I'm at the moment studying to take the TOPIK (Test of Proficiency in Korean) next Sunday, and my goal is to pass Level 3 of 6. Not super high, but I'm about at that level despite living in Korea for just shy of seven years.
My parents both speak Spanish (they met at a Peace Corps recruiting seminar, where they were both speakers about their experiences - Dad in Bolivia and Mom in Peru), so I picked up a smattering as a kid. Slightly more than the average American picks up due to what's been appropriated into U.S. English. Not a lot.
In High School, I took two years of French. I don't remember much, but every now and then I can figure out a bit of written French on the side of a cafe's mug or on someone's t-shirt. [I may be a 4th level Thief?]
In college, I took a year of Spanish, but I was in the non-major/minor course, with all the soccer players and whoever just needed some language credits to pass. Using my childhood vocabulary and high school French vocab/grammar, I got "A"s for two semesters, and my Spanish is about as poorly developed as my French.
After suffering/coasting through those two Spanish courses, I switched to Japanese. Talk about a change! Japanese was a challenge, but I persevered through three years (six semesters) of Japanese. Then I went and lived in the country for a decade. During that time, I managed to pass Level 2 of the JLPT (Japanese Language Proficiency Test) [In Korea, high is better, while in Japan low is better]. Not too shabby. If I hadn't been lazy, I probably could have improved to JLPT Level 1 (near-native level). But I was lazy and Level 2 is pretty darn good for someone not working in translation or other fields where mastery of the target language is necessary.
When I hit Korea, my first son was just about to be born (my wife, who is Korean, wanted to be with her family when she gave birth so we left Japan), and I entered an intensive Korean language course. For 20 weeks, I crammed two years worth of Korean study into my head. It was too fast of a course, and spending three months back in the States after it didn't help cement what I learned in my mind. I've struggled to improve my Korean, but the struggle is mostly one of motivation. Koreans don't seem as willing to help foreigners learn their language as the Japanese are, and with my wife as a crutch, I can get by on my just barely TOPIK Level 3 language ability.
Why all the personal history of my language study? How does this apply to gaming? Yes, I'm finally getting back to that.
If I were an RPG character, which of these languages would be on my character sheet? I'm functionally fluent in Japanese, so that would definitely be there. How about Korean? I'm able to perform basic functions in my day-to-day life, sometimes with a bit of effort. But I only get the gist, if that, of what they're talking about on the news or the plots of TV dramas. Is that enough to count in a binary "know it/don't know it" system like D&D? French and Spanish are languages I'm only passing familiar with. They probably shouldn't be on the sheet. But yet, every now and then, I can understand a bit, or remember a song or a few basic sentences. If I were to travel to a country that speaks either language as a tourist, I'd have few troubles shopping, finding landmarks, etc.
Now, here's the real question. In an RPG, is this level of granularity of detail worth the effort it takes to implement? Does it add to the fun of the game?
Miscommunication can be a good tool for creating dramatic tension or comedy, but is it fun at the table? Would a system of unfamiliar (0), familiar (1), functional (2), fluent (3), native (4) be worthwhile?* How to adjudicate it? How to keep it fair when the DM can just decide that while my Harpy is "functional" the harpy's Common is "native" so we just use Common? How do we adjudicate miscommunications when the goblins are yelling at us, but my Goblin is only "familiar"?
I think the answer lies in the fact that for forty years now, D&D games have been going on just fine with a binary "know it or not" system of language. Just like how on TV, the aliens or foreigners always seem to speak English, it's a convenient time-saving device that allows us to get on with the fun, rather than stop the action to figure out just how much of your broken Giantish the Frost Giant understands before he tries to pound you into pulp.
*I remember reading a system like this either in a d20 game, or just as a home brew system to implement for d20 games on, I think, the Wizards.com forums back in the heyday of d20 System.