I’m trying to find the perfect love song - a song that…
I know how subjective all of this is, and will treat each suggestion with respect.
I really like for a love song Adore. It does mention sex but it’s not explicit. It’s a beautiful song.
I believe the New Musical Express in the UK voted Northern Sky, by Nick Drake, the greatest love song of the 20th Century. I’m a Nick Drake obsessive, so I agree. It’s tremendously subtle - maybe too subtle for your purposes - but it’s simply beautiful. Lyrics here.
Alternatively, Ewan McColl’s The First Time Ever I Saw Your Face is also painfully lovely, with Johnny Cash’s version being the best I’ve heard.
I was going to mention The First Time Ever I Saw Your Face. It’s a beautiful song. Celine Dion’s covered it so that ups the sappy factor, I suppose. One of my current favorite love songs is nice simple one called Grace by Me’shell Ndegeocello although it’s not quite up there with The First Time…
I’ve got a bit of a soft spot for Everything, by Michael Buble. I won’t try to strong-arm anyone into sharing my opinion on it, but there’s pretty much nothing in this song I don’t really like.
I agree with jjimm for The First Time Ever I Saw Your Face, though I prefer Roberta Flack’s version.
I’d also nominate I’m Your Man and Dance Me To The End Of Love. Awesome songs by an awesome musician.
And it’s more tenderness than sexual tension, but I’ve always considered Simon & Garfunkel’s Bridge Over Troubled Water as one of the most beautiful love songs ever.
For all of me there’s no need to write anything after Dire Straits ‘Romeo and Juliet’.
Love song-The Cure.
Although I am going to link to 311’s version, it’s a little more interesting.
Bonnie Raitt’s version of Feels Like Home. (I really only linked to this youtube video for the song, not the video.)
You’ve just got to read the lyrics. I nearly melt everytime I hear it. Ok, I’m sappy, but the song, not so much. 
I think two from Wilco would fit the criteria. We’re Just Friends has some sexual tension, isn’t sappy, and makes it clear that there is an intense love between the two people, even if it’s unrecognized or not consummated.
I’ll come back to you
It’d be brand new
But I promise
We’re just friends*
A lot of the emotion in the song is in the way Jeff Tweedy sings it.
The second nominee is Either Way. It strikes me as one of the most mature love songs I’ve ever heard. The message is simple and straight forward, without being angsty or over-wrought.
ugh. I feel so old school…
I’ve always liked Meatloaf’s “Anything for Love” (especially amusing as a DrPepper commercial), “Because of You”, “I’d Lie For You” and “You Took the Words Right Out of my Mouth”
More up2date: Carbon Leaf’s “Life Less Ordinary” - nothing sexual in that song though.
On a completely different tack: The Liebestod. Here’s a translation.
This is one of the few things that will almost reduce me to a useless lump every time I hear it.
If you’re not familiar with the plot (it’s from Wagner’s Tristan und Isolde), this is from the very end, where Isolde literally wills herself to death in order to join her lover in the ultimate expression of love; the ultimate orgasm (petit mort), as it were.
My all time favorite: “I Will” from The White Album.
George and Ira Gershwin’s They Can’t Take That Away From Me
Has everything you mention in the OP and, as a bonus, the music is by George Gershwin.
Not sure about sexual tension, but the one that usually reduces me to a puddle of mush is Ben E. King’s Stand By Me.
I’ll think of some other, nontraditional ones later. You’ve set the bar really high, Nature’s Call!
REM - Perfect Circle
…romance…
Pixies - Cactus
…mad sex…
The Stooges - Dirt
…disillusion…
The Birthday Party - Deep in the Woods
…the inevitable murder…
The Carpenters - Close to you
…reconciliation in the afterlife…
“The Look of Love”, especially the original Dusty Springfield version from Casino Royale. She released several versions, but that’s far the best. Music by Burt Bacharach, lyrics by Hal David.
Most love songs, “The Look of Love” included, are actually lust songs. (They haven’t yet been together in that song. No song about *wanting * a person is about love. Love is about being with a person. Accept no substitutes. 
) But the best true love song in rock is John Sebastian’s Darling, be Home Soon. Notice that the lyrics are about talking rather than sex, although the undercurrent of sexual tension is implied. Interestingly, it’s also from a movie, You’re a Big Boy Now.
Good point.
Unless someone is in the process of losing a person they love.
*Ne Me Quitte Pas - * Video Jaques Brel (4 min 12 sec) with free French - English lyric translation.
Here and Hereafter (that’s an authorized mp3 download)
This song works on several different levels. On the top surface it’s a breezy love song, maybe even a bit corny.
Dig a little deeper and the musical and vocal layers start to reveal themselves. Dig even deeper and it’s actually about how terrifying it is to be in love, because then you have to deal with the fear of losing that person.
not 100% sure this is what you are after but
http://www.lyricsdownload.com/kd-lang-so-it-shall-be-lyrics.html
K.D. Lang from her Ingenue album