Seriously? You do know that this is not a lovesong?
Kenny G’s Wedding Song is also very nice
It would be nice to find some songs with a personal touch as well. We had selected China girl (David Bowie) and Blue eyes (Elton John) representing bride and groom. We also included Reality, because the lyrics were highly appropriate (Met you by surprise, did not realise that my life would change forever…).
Um, I’d definitely check into “Sweet Jane.” If The Velvet Underground’s version (Make sure you get the one on the “Fully Loaded” edition of Loaded, it’s got the “Heavenly wine and roses” bridge) doesn’t tickle your fancy, try The Cowboy Junkies’. I’m pretty sure everyone loves that song. I’d also highly recommend Cassandra Wilson’s cover of Van Morisson’s “Tupelo Honey.” At least, these are two songs I want at my wedding.
Wild Horses by the Rolling Stones
Kissing You (Love Theme from Romeo and Juliet) by Des’ree
Hooked on a Feeling by B.J. Thomas
You Spin Me Round (Like a Record) by Dead or Alive
Both Hands by Ani Difranco
Wild Horses by the Rolling Stones
Kissing You (Love Theme from Romeo and Juliet) by Des’ree
Hooked on a Feeling by B.J. Thomas
You Spin Me Round (Like a Record) by Dead or Alive
Both Hands by Ani Difranco
Let us know what you decide!
Wow you are getting some great responses, Dont forget Unchained Melody and this also played at our wedding we are family. My husband and I both bolted from the room we hate that song!
What?!? No country music? It ain’t popular but it is loaded to the hilt with romantic Lyrics
Just look at Us/ Vince Gill (this guys got a million of them)
The Dance/ Garth Brooks
My own wedding dance was Barry Manilow’s When October Goes. A dinner Jazz type tune, lyrics by Jonny Mercer
*** Chorus Lyric ***
And when October goes
The same old dream appears
And you are in my arms
To share the happy years
From this moment Shania Twain
Don’t want to miss a thing Aerosmith
Because you loved me Celine Dion
Could I have this kiss forever Enrique Iglesias
All my life KC & JoJo
I want to be with you Mandy Moore
When you say nothing at all Ronan Keating
Love is in the air (Erm… you know the one… from Strictly Ballroom)
Hope we’ve helped, even if only a little bit 
Will His Love Be Like His Rum? – Harry Belafonte. The lyrics are a hoot, and it’s a fun, upbeat song: “Drink, drink this toast. Drink this wedding toast! Drink, oh, drink this toast to the two we love the most.”
With You – Peter Himmelman. This is the song my husband and I danced our first dance to: “With you, I can speak with a voice that rings with love and mercy.”
The Way You Look Tonight – Frank Sinatra. A classic.
My husband also wanted Elvis’ Caught in a Trap.
Nothing Compares To You-Sinead O’Connor
Got To Get You Into My Life-Beatles
When I’m Sixty Four-Beatles
Somewhere Over The Rainbow-Israel Kamakawiwo’ole
And for a laugh
The Lady Is A Tramp-Sinatra
Having My Baby-Paul Anka
I Touch Myself-Divinyls
Why Don’t We Do It In The Road-Beatles
Arrgghh!! I’m going to get bitchy here for just a second. Just because a song is slow, that does not make it a romantic song that is good for a wedding.
The Dance - About losing a love and being happy for the time they had spent together
Every Breath You Take - About stalking
Nothing Compares To You - About being miserable because she lost her love
Again, I’m sorry and I hate when someone comes in to rain on the parade, but this one just drives me nuts!
Ah, monster, but, some of those songs do meet the conditions of the original post. They didn’t say anything about POSITIVE songs about love and romance.
Besides, how often do people really realize what the songs are about?
Good point, photopat! I guess I just assumed they want “we’re in love” songs rather than “you’re gone, so I’m miserable and going to stalk you now” songs. 
There’s a difference? (Kidding, I’m kidding)
If I Had The World To Give by the Grateful Dead. IMO a very pretty love song. Lyrics can be viewed here.
I apologize if some of these have already been listed, but how about:
love will never do (without you) - Janet Jackson Design of a Decade
Peaceful, Easy Feeling - The Eagles Their Greatest Hits 1971-1975
Fever - Peggy Lee
In Your Eyes - Peter Gabriel from the * Say Anything* soundtrack
Love Theme from Bladerunner - It’s instrumental but extremely romantic! You could play it for atmosphere.
Ring of Fire - Johnny Cash Love
Glory of Love - Peter Cetera Solitude/Solitaire
Bridge Over Troubled Water - Simon & Garfunkel Bridge Over Troubled Water
The House You Live In - Gordon Lightfoot Summertime Dream
Love is All Around - REM (I believe it was only released as a single) or if you can find it the a capella version by The Flying Pickets
Crazy Love - Bryan Ferry on the She’s Having a Baby soundtrack
I will love you - Fisher
At Last - Etta James
Love and Honesty - Hawaiian Style Band
a beautiful slow song, little of an island feel in the lyrics
“This I promise you” by NSYNC
“Thats when I’ll stop loving you” by NSYNC
“I wanna love you forever” by Jessica Simpson
“A walk to remember” by Jessica Simpson
“I turn to you” by Christina Aguilera