While I don't really have the patience or time to be actively studying a new language, I too really like to discover new cultures and learn new languages. The language itself usually teaches you a lot about how its users view the world.
My main languages are Dutch, English, French (I haven't spoken it in years, but I still understand everything easily), C#, Java, C(++), HTML, you know, general stuff.
I know some dead languages too, like a bit of Latin (used to be a lot, but my memory is terrible) and old Greek... and even some Classical Chinese. I had the pleasure of studying that last one for a few months at university. For all of those, I think the main interest I took in them was not the language itself or the culture, but the stories and the poetry. Some of these stories paint worlds that just don't exist in modern literature, and some poetry from back then shows how much the world hasn't changed in all this time.
It's also very nice if you can study a language like this at school: education programs for modern languages usually have you simulate boring casual conversations in class, but those for dead/classical languages have you read huge epics like Homer's Iliad, or translate (and almost sing) poetry about passionate love, or be spirited away to Chinese gardens to ponder on the meaning of life. And while doing so, especially with Latin and Greek, you learn about the origins of so many modern languages, you get to understand all the difficult words in your language you've never heard before without having to look them up.
As for modern languages, I've been very interested in Japanese for quite a while. Since I started anime ~6 years ago (and kept watching like almost every day), I've picked up quite a lot of the language. Granted, it has a lot of similarities with that Classical Chinese I learned, but most of my knowledge comes from anime. Most people laugh at you when you say that, but it has enabled me to understand conversations of Japanese tourists, or watch anime without subtitles, for example. I'm fairly sure I can speak it a little bit too without sounding like an idiot... but writing is a different story. The strokes system is pretty much the same as that Classical Chinese I learned, but memorizing all those kanji would take up so much time. If I ever learn to manage my time better though, who knows... I might try it out.
