I've encountered many languages in my life, as I've always lived very close to an internationally popular tourist destination. I'd love to learn them all, but unless you're Dr. Daniel Jackson (Stargate reference), then that's a near impossible goal. I'll do a bit of a breakdown here of some of the languages I'd like to learn if I had the time and unlimited mental capacity to learn them all.
Japanese (日本語)
This language I am already learning. I find it very interesting, and with the boom of anime and manga popularity here in North America, I decided to learn it. I've been studying a little at a time since last June. I've greatly increased my listening comprehension by watching Japanese Dramas, but my speaking, writing, and reading all need work.
French (Français)
I already know quite a bit more French than I think I do. Canada is a bilingual nation, so everyone is made to learn French and English in school. Some schools teach more of it than others. I was personally always pretty good at French by comparison to my classmates, though I never really noticed at the time. I'd have to brush up on my grammar just a little to use my French, and study a lot of vocabulary, so that I can actually say what I'd want to say.
Chinese and Korean
I love the sound and written language for most Asian languages. I hear Chinese is very difficult to learn, as pronunciation is important to the extreme. Still, if I had time to learn many languages, Chinese and Korean would both be high on the list. Chinese would also likely be easier to learn after learning Japanese, since I would already have studied a variation on the writing system.
Arabic
I know very little about Arabic, but I once took a summer school class with a student from Egypt, whose native language was Arabic. He tried to teach me a bit, but I don't remember any of it. The writing system is nifty. I have a fascination with writing systems, really. I'd love to learn any language that doesn't use Roman characters, and some that do as well.
All Others
The above are just Languages that I know I want to learn. Really, I just want to learn every language in the world. Oh, and throw Russian on there so that I can chat with any Astronaut on the space station. 