I bought the soundtrack to Bram Stoker’s Dracula specifically for this song. I’m so happy you mentioned it.
The emotion in that song - its so exposed and raw. Very intense. At least that’s what I get from it. 
This suggestion made me laugh and I may have to use it just because my friends would crack up. They all know me too well. 
With all the great music here I am going to have enough for several receptions. I haven’t decided which songs I am going to use from the ones mentioned here but some of the ones I was already planning on using are:
“Ice Cream”-Sarah McLachlan
“Luna”-Smashing Pumpkins
“I Could Die For You”-RHCP’s
“In The Mood” and “Sentimental Journey”-Glen Miller
“Stickshifts and Safetybelts”-Cake
“Two Step”-DMB
“Kissing You”-Des’ree
“Carry You”-Dispatch
“At Last”-Stevie Nicks version
“Landslide”-Fleetwood Mac (for my dad)
“Ball and Chain”-Social Distortion 
“Kind and Generous”-Natalie Merchant
“Castles Made of Sand”-Tuck and Patti
Some Eva Cassidy, Norah Jones and various other stuff that I can’t think of right now.
Thanks again for all the great suggestions from everyone.
I can’t imagine how you’d ever find it…
but if you can get a copy of a CD called Flat World by a band called Stranger than Pretty (really a woman called Claire Harding, who seems to be on the faculty of the All Newton Music School in Newton, MA, now), the song “It Never Gets Better (Than This)” is the best love song I have ever heard.
Nobody’s mentioned Sam Cooke?
You Send Me
(I Love You) For Sentimental Reasons
Cupid
Nothing Can Change This Love
Wonderful World
You Were Made for Me
All wedding-appropriate Sam Cooke classics.
A few more:
Up on Cripple Creek - The Band (This one will take a sense of humor)
This Magic Moment - The Drifters
It’s Oh So Quiet - Bjork
There Is a Time - The Dillards (bluegrass classic, if you want to mix things up)
Ring of Fire - Johnny Cash
Love Me Tender - Elvis Presley (come on…you gotta have some Elvis)
Teddy Bear - Elvis (some danceable Elvis)
Oh Boy! - Buddy Holly (speaking of danceable)
True Love Ways - Buddy Holly
How Do You Fall in Love - Alabama
Grow Old With Me - John Lennon (being sung at my wedding)
pulykamell and Tracy Lord - I’m actually having God Only Knows sung at my wedding this fall.
Suddenly Seymour - Little Shop of Horrors.
No really, it’s good!
Anniversary Song- Cowboy Junkies
Call My Name-Prince (some serious funk here, use at your own risk)
My One and Only Love-Sting cover
Flowers in the Window-Travis
Always-Stevie Wonder
The Truth-India.Arie
By Your Side-Sade
A Sort of Fairytale- Tori Amos
I love Stevie Nicks and her version of “At Last” is great BUT the difinitive rendition of this song is by “Etta James”. So help me! If you havent heard it, find it, give a listen before you finalize your list. I plan on using it for the same purpose in the near future.
At Last
Longer Dan Fogelberg
- we’ve only just begun* Karen Carpenter
The First tTime Ever I saw Your Face Roberta Flack
Our House Crosby, Stills and Nash.
I won’t last a day without you Barbra Streisand
Page nine Janis Ian (Will you really come and live with me? We can watch TV when the nights are cold and its hard to sleep…)
I love Etta James and everything she does, including “At Last”, but I am going to be using Stevie’s version for personal reasons. But not to worry, Etta will have a prominent place at our reception.
Yes. Most definitely. Came here to mention it and what do you know? Its already taken care of 
One more…And Forever, the end-titles music from the anime series Big O. (The uncut version, 'natch.) It takes a little looking, but you can probably find it.