English, it’s the only one I understand… usually.
I feel similarly about Portuguese…sounds like Italian with a French accent.
Another vote for Russian, I also love to hear Russians speaking English.
“We must get Moose and Squirrel.”
Vote for Russian.
You’d probably expect me to say Chinese, but I think Italian sounds gorgeous.
Portuguese. There’s a reason why the number-one non-English language heard in Jazz is … Portuguese.
French and Italian are right up there.
At work I occasionally deal with project teams in foreign lands, and I love having meetings with the folks in Canada (Quebec), France, and Italy. Though they only speak English in the meetings, their English has such a beautiful accent.
Ladino.
My inlaws speak it, and while they do it mainly to annoy me, it’s still a beautiful language.
I would say this as well. I am Spanish, and when I hear Ladino spoken, it is really a bit of a “shock”. Like being transported back in time to the 15th-16th centuries. Ladino keeps sounds and structures of Spanish as it was spoken 500 years ago. Listening to Ladino is like listening to Spanish as Don Quixote would have spoken it. It is positively charming and fascinating, at least for a native Spanish speaker!
<slight hijack>Does Yiddish have this kind of effect on a native German speaker?</slight hijack>
<Revenge of the slight hijack>There is an anecdote that, although unrelated to the subject of the thread, is very funny and ties with the subject of Ladino language. Apparently, in the early 20th century, there was a Spanish catholic priest who went to Thessaloniki. Two Jewish sephardi women heard him speaking Spanish, and automatically assumed that he was Jewish 
They marvelled at that, and said to each other: “Look at that! a Jew who is a pope!” (“pope” here in the sense of an orthodox priest)</Revenge of the slight hijack>
I’m Italian, but it’s such an ugly language. How about… Russian?
Varrtina are Finnish! And if I’m not mistaken they sing in Karelian, which is, wait for it, a Finno-Ugric language. But it is definetely closer to Finnish than to Icelandic.
Personally, I like Spanish and Italian, but actively dislike Portuguese. Arabic also sounds good to me, very passionate.
I love English, honestly, and I do listen to lots of other languages and love them, too. But there isn’t anything that sounds better to me than plain old English.
Japanese is a close second, though. Urdu is beautiful in poetry, nothing like it.
Icelandic. Its beautiful. Listen:
I also love Hafdis Hulds singing, though she sings mostly in english.
I’m surprised as well that nobody has mentioned Irish, a very lyrical and pleasing language.
French is just a susurrus to me - I can’t make anything out. I like to listen to German, and some Native American languages (I don’t even know enough to know which ones, but some Native American chants are hypnotic).
Portuguese is a beautiful language. It makes me cream my pants when I hear it.
Swedish, Finnish, and Tamil are my favorites (in this particular regard).
Busuu!!! 
Spanish.
You could play a video of a young Latina woman describing how she’s going to wallpaper her bathroom, but to me it would sound like Liquid Fuck™.
Similarly, I knew an Italian women who could read the ingredients off a Twinkie wrapper and it would be sexy.
I’ve described the Frenchwoman who sat in the cubicle next to mine at my old job, and whose voice it was exquisite pleasure and torture to hear.
So, I’m prepared to say that it’s not the language that sounds best, but the person.
Edit: that being said, I kind of like Finnish.
Here you go Walmarticus: Elis Regina singing Águas de Março
(Wikipedia sez this tune “was named as the all-time best Brazilian song in 2001 in a poll of more than 200 Brazilian journalists, musicians and other artists”)
I think Spanish sounds sexy, but I would rather listen to someone speaking English with an Irish or Scottish accent.