[Raion]

So yeah, if you have little to no preexisting knowledge of a language, that counts
 
I can name a few:

Afrikaans - My choice because what I know about it is that it is like a mix of Dutch and English due to the shared history of South Africa

Korean - I know little of Korean other than sino Korean cognates and food terms. The pronunciation intimidates me.

Maltese - Is a variety of Arabic with Italian influence which is freaking interesting. Also written in a script I understand

Hebrew - The biggest language that was revived from liturgy usage into an official language including a sign language. 

Sardinian - Supposedly closest Romance variety to Latin, which I've learned a decent amount of. 

Vietnamese - I would especially wanna learn Chu Nom, the Chinese writing adapted to Vietnamese.

[Shiunbird]

Xhosa - the click sound fascinates me, it's very melodic and biased by the voice of Miriam Makeba
Korean - I find the script so interesting.
Latin - started a million times, never continued, just not enough time during the day.
Greek - for the classics.

[jan-jaap]

Greek - for the classics.

Ancient Greek appealed to me in high school because it's like math: there are only rules and no exceptions

[jpstewart]

Greek and Latin always struck me as interesting since they have such long histories and form the basis of so much.

German always struck me as a good one to learn, but I can't really give any reason for that.

I'm a native English speaker with modest skills in French, but I'd always wished I could have been the type of Canadian who is fluently bilingual.  But in my town there's little to no use for French so I've forgotten most of what I learned in the past due to lack of practice.  Still, even though it doesn't fit the criteria "that you have little knowledge of", it would be top of my list to get much better in French before any other language.

I know a lot of our forum members aren't native English speakers yet they manage to communicate here just fine.  And I'm jealous of all you folks who can use multiple languages.

[lunatic]

an old item on my list that I never fully mastered:

APL

[jpstewart]

Another one I should have mentioned previously:  sign language.  It seems like it would be both fun to learn and very useful in the real world.  (Yes, I know there are many different sign languages in use around the world....)