I am a big fan of the Scandinavian languages, such as Norwegian and Swedish. They sound wonderful.
Welsh is the first thing I thought of when I saw the thread. Don’t even ask why I didn’t put it first in my actualy reply, please.
Russian sounds interesting and fluid, and I love it.
I’ve never heard the poetic Urdu being talked about here, but I really want to after reading this topic.
I seem to have a lot more limited exposure to languages than I thought before I opened this thread. You all seem to have heard lots of different languages.
I used to like Japanese before learning it, and I liked it better while learning it than I did after I moved to Japan. Now, I’m tired of hearing girls squealing “kawaii, sugoi!” all the time. I know a couple of women who speak in lower, more attractive registers, but they’re all old enough to be my mother. Kabuki and old-style story telling is very nice, as is poetry. Yakuza influenced Japanese sounds either incredibly tough or trashy, depending on the situation.
Mandarin sounds pretty darn cool to me. Hero, Farewell, My Concubine and Crouching Tiger, Hidden Dragon should never, ever be released in a dubbed version. There should be no choice but subtitles.
Irish Gaelic is an interesting language. Lots of liliting tones mixed with gutterals.
Finnish left an impression on me. Of course, that might have had a lot to do with who was speaking it. Man, was she hot!
Persian poetry sounds best of all to me. I put Persian at the top of my list.
I agree Mongolian sounds really nice too.
Swahili is one of the sweetest sounding languages ever. It just flows so smoothly and gracefully.
I used to love Hungarian Hour on the ethnic radio station in Cleveland, because the lady talking in Hungarian articulated it with a gentle, rapid staccato that sounded like rain on the roof. Tamil has this interesting quality too, but with a different set of sounds and more pitch range.
Scots/English 
I’m gratified to see all the votes for Italian. Is anyone counting the votes? I think Italian is in the lead so far.
The sound of a Persian woman speaking Persian is the ultimate linguistic ear candy for me.
J.R.R. Tolkien thought Finnish and Welsh were the most captivating languages he knew, so he modeled Quenya and Sindarin to resemble their sound.
[symbol]Zwh mou, saV agapw[/symbol]