“Head” by Prince.
Actually, pretty much the album “Dirty Mind” in its entirety.
David Cook, this year’s winner of American Idol, has a voice that is very sexy to me; him singing “Music of the Night” is definitely in this conversation.
My choice for “sex on a stick” song - Toni Braxton “You’re Making Me High.”
My husband’s choices - “Don’t Let Go (Love)” by En Vogue, and everything by Prince. 
Some more specific Prince songs - “And God Created Woman,” “Damn U,” “Anna Stesia,” “I Wanna Melt With U,” “Incense and Candles,” “Ripopgodazippa,” and, of course, “Orgasm.” 
(Looking at my Prince playlist, I think my husband was right the first time. )
Oh yes, Except! by the original female (who? somebody help me)
Off to think of some more
Patti Smith
Although already mentioned at #15, Slow Hand by the Pointer Sisters is my most sensuous song of all time.
Followed by Chicago and “Hard to Say I’m Sorry”
I was also going to say “Because the Night” as well. I know it is heresy but I like the 10,000 maniacs version with, who is it? Natalie Merchant, version much better than Patti Smith.
I thought of another one. “Ex-Lover’s Lovers” by Voltaire. The song itself isn’t sexy at all - it’s about him resenting his breakup and plotting to kill his…well, look at the song title. But his voice! Og, I could listen to him whisper about cutting me up for days. Rowr!!
I was just on hold at the pharmacy (migraine, cf. mini-rants in the Pit) and heard what had to be Aaron Neville singing John Hiatt’s “Is Anybody There?” Yowza.
Hmm, didn’t know it was a cover. Now I have to go find the original. BRB.
Nope, I like the 10k Crazy People version better.
Radio station reminded me this morning about Marvin Gaye’s “Let’s Get It On”.
Definitely the Natalie Merchant (Unplugged) version of Because The Night.
Thought of some more:
Bauhaus’ Nerves and Third Uncle (it’s in the dirty, dirty rhythms)
and Pixies’ Debaser
IS it my imagination, or has this thread attracted an EBM/Goth majority? Think it was the OP’s examples that did it? (Oh, and thanks, OP, for the Birthday Party vid. Hadn’t actually thought to look for them on youtube. Zoo Music Girl is my favourite Cave song ever, closely followed by Sonny’s Burning. I mean, I like Bad Seeds, soundtracks and other stuff he’s done a lot too, but there’s something about someone shouting “Hands Up Who Wants To Die!!!” that makes me feel 18 again.)
Oh hells yes.
Nick Cave: “Do you love me?”
Me: “OMG YES!!!”
The Faint - Worked Up So Sexual.
Dayumn!
“Brass in Pocket”, especially the live version on Isle of View.
“Be My Baby,” by the Ronettes
“You’ve Really Got a Hold On Me”-Smokey Robinson
“Cruisin’”-Also, Smokey Robinson
Madonna.
Dick Tracy.
Sooner or Later, 0:40 through 1:08.
Had to leave the theater for a bit.
Lovedrug “Happy Apple Poison”
Adam Cohen “Don’t Mean Anything”
Greg Dulli “Early Today”
The last two songs are by guys who aren’t much to look at, but have voices that make you want them anyway.
Oh yes, I agree 100% especially on the Anywhere song. A lot of songs from the 90s are like that for me though. Silk, Intro, R. Kelly.
The Transitions - Straight Fuckin’ is one I stumbled upon recently that well … yeah.
For some reason “Cowboy” by Kid Rock always wants to make me give Himself a lap dance. Not 100% sure why, though.
“Closer” by NIN as mentioned earlier.
“Bad Bad Thing” by Chris Issak
“Woke Up this Morning” (the Sopranos theme)
“Bad Touch” by Bloodhound Gang
I have a couple more, but they would also reveal a trend. 
I actually made myself a CD of songs that fill this category; this is just a sampling.