I like this one alot, especially as it’s my second marriage.
“When You Say Nothing at All” by Ronan Keating is also high on the list.
Thanks, keep the suggestions coming, please. Not meeting the DJ until after Christmas…
The Luckiest was our wedding song 
I’m partial to “Paradise by the Dashboard Light” followed by “Having My Baby” (or, alternatively, “Brick” by Ben Folds Five, although that’s less likely to end up at a wedding).
We chose the Eric Clapton & BB King version of “Come Rain or Come Shine” for our upcoming wedding. Another situation where we don’t really have “our song” so we had to hunt something down that we both liked and could dance to. When my man showed me this one, I knew right away it was perfect. It’s “us”, somehow. The right sentiment, and right style… I can’t wait for the wedding so we can dance to it!
Jack Johnson, “Do You Remember”
It’s not our wedding song (we didn’t have one), but it’s become “our” song. (The previous “our” song was “What I Like About You” by The Romantics.)
However, “Do You Remember” is pretty short - it’s not much longer than 2 minutes or so. But the lyrics are awesome.
I’m also thinking of wedding songs, so I’m reading this thread with interest. My current favorite is Smile by Uncle Kracker (3 minutes, 22 seconds):
You make me smile like the sun
Fall out of bed sing like a bird
Dizzy in my head spin like a record
Crazy on a Sunday night
You make me dance like a fool
Forget how to breathe
Shine like gold buzz like a bee
Just the thought of you can drive me wild
Ohh you make me smile
Maybe I’m being whooshed here but wouldn’t any of these songs be unlikely choices at a wedding? (Not to mention that “Paradise” isn’t a ballad.)
“Bubbly” by Colbie Callait
“How Sweet It Is” by Michael Buble (or James Taylor)
Depends on the Style of Music you are playing
Country/Western
“Could I have this dance?” - Anne Murray
“I Do, Cherish You” - Mark Wills
R&B
“Spend my life with You” - Eric Benet and Tamia
“Always and Forever” - Heatwave (NOT LUTHER)
“Endless Love” - Lionel Ritchie and Diana Ross
Rock
“Don’t Want to Miss a Thing” - Aerosmith (Yes, it’s a power ballad, but it’s good)
My musical brain cells are fuzzed right now… i will think of more.
I must respectfully disagree with you, ministryman - “Don’t want to miss a thing” is one of the worst songs ever recorded." 
We used “Suddenly” by Billy Ocean for our wedding song. Now there’s a forgotten classic!
•“Orchestral Suite from ‘The Inner Light’”
•“Labor of Love”—Michael Giacchino
•“Together”—Robotech Soundtrack
•“That’s All I’ve Got to Say”—The Last Unicorn soundtrack
•“My Own True Love”—Nana Mouskouri
•“And Forever”
•“Bridal Ballad”—Hayley Westenra
Slow - “Something” by The Beatles.
Quick - “Best Friend” by Queen.
I second* Smile *by Uncle Kracker. One of the sweetest songs I know.
This was probably the biggest bone of contention for me and the (now) wifey 
I was actually taking the super-romantic side, she was taking the super-silly.
We ended up starting off with Edwin McCain - I Could Not Ask For More, and then suddenly switching into You Never Can Tell by Chuck Berry.
I also lobbied (obviously unsuccessfully) for Billy Joel - To Make You Feel My Love.
Smile by Uncle Kracker features the line:
“Cooler than the flip side of my pillow”
Now that is how to turn a phrase!
If you’re still in the market for James Taylor, though (he’s been mentioned a couple of times in the thread), may I nominate: Something.
OTOH (the other other hand?) I’ll Stand by You by The Pretenders.
Hubby and I tango’d to Louis Armstrong’s Kiss of Fire for our first dance. Sexy and romantic at the same time.
That song totally describes our relationship
Glee ruined “I’ll Stand By You” for me as a wedding song, IMO.
I’ve always favored Armstrong’s “We Have All The Time In The World,” although for anyone who has seen On Her Majesty’s Secret Service (for which it was written) it will have ominous connotations.
Stranger
Some friends of mine just got married and they used a song, written by Steve Martin and sung by Vince Gill and Dolly Parton called 'Pretty Flowers"
http://www.the9513.com/spotlight-steve-martin-featuring-vince-gill-and-dolly-parton-pretty-flowers/
I would use Jonathan Coulton’s Skullcrusher Mountain.