If You Want My Love - Cheap Trick
Come and Get Your Love - Redbone
Alison Krause - When You Say Nothing At All
Everything - Alanis Morissette
Sweet Child O’ Mine - Guns N’ Roses (the verses are actually pretty well written)
I Try - Macy Gray
I’m sure I’ll think of more…
Most of my favorite musicians don’t have many love songs, but I culled and found some that are close. It was tough. Kate has 8 albums, and I could only think of a handful that are love-type songs. Same with Hap. 11 albums and, damn, it was hard to find love songs. Mostly these women tell stories or sing about personal, non-relationship matters. I can provide you with free mp3s if you like any of Hap’s songs because I have permission to do so, but I can’t help with Kate.
Kate Bush
“The Man I Love” (killer Gershwin cover, with Larry Adler on harmonica, a breathtaking Kate)
“Eat The Music” (love/fruit/music metaphors, voodoo, wild dancing, a beautiful Kate…that’s Lindsey Kemp at the beginning, he was in the original The Wicker Man as Alder MacGreagor, the Innkeeper, Britt Ekland being the Innkeeper’s daughter. It seems out of place because it comes from a long-form video called The Line, The Cross and The Curve, starring Miranda Richardson, Kate and Kemp. This is the official video, different from TLTC&TC, and I don’t know why they didn’t cut that opening out. Oh well.)
“Why Should I Love You” (demo version, before Prince ruined it)
“Pi” (a love song about a guy who loves Pi)
“The Saxophone Song” (a love song to a guy who plays the saxophone)
“Houdini” (Mrs. Houdini’s love for Mr. Houdini)
“The Man With The Child In His Eyes” (an early song, some consider it a love song)
“Oh To Be In Love” (an early song about being in love)
“Under The Ivy” (giving a lover a very precious gift)
Other songs that might seem to be about love really aren’t, like “Hounds of Love” or “Love and Anger” or aren’t suitable for this thread, like “L’Amour Looks Something Like You” or “Mrs. Bartolozzi.” Lots of other songs are about creepy or bizarre or dangerous kinds of love, again, not suitable here.
Hap (all vocals on all songs by HTR)
“Hold Me” (David Torn on Electronic Guitar)
(Here is a slower, quieter, more acoustic version, and here’s a live version [fanwank]where she forgets the lyrics and looks at me to provide them[/fanwank])
A few very old songs from when she was very young, so maybe not mature, but I can’t not include them.
“Come Here” (sweet waltzy song, don’t let the monster scare you, he’s a very nice monster)
“One Alien” (unusual viewpoint, but still a love song)
“If Love Is A Game, I Win” (another sweet song, another nice monster, don’t freak)
Really wacked/unusual viewpoints, but still love songs, in a way.
“Here And Hereafter” (can be heard as a beautiful and breezy love song, unless you really pay attention, so don’t. Just enjoy)
“Number One” (very old, another monster)
“Case of Glass” (well, it’s very sweet for a mini Twilight Zone episode…)
Stretching:
“Omar” (kinda love-songy, a love letter to Omar Sharif, though he’s not specified except in the title, so it could stand in as a regular love song.)
“He Will Come/The Flight” (ok, it’s a 2-part vampire love story, so it may not count)
“The Wretches Gone Awry” (a love song to wretches, and they need love too)
People have posted some great songs. I actually went and looked through my whole collection before I looked at the rest of this thread, and found it surprisingly difficult to find any such songs–maybe I’m sadly cynical, or just too young. Or maybe I’m paying more attention to the realistic/mature part than others… I only found a few songs and someone already mentioned one of them. (Wilco’s “I Got You”).
The other one is a bit of a long shot–not to everyone’s taste, but some people love her (like me!) She’s an amazing lyricist.
Joanna Newsom - Good Intentions Paving Company
If you really want something from every genre, I like the Roots / Erykah Badu “You Got Me.”
‘You’re My Best Friend’ by Queen. What better way to say ‘I love you’?
All of these songs are from the wedding CD we made for a wedding favor for our guests (tried to focus more on the songs for your theme, we had some over the top gushy ones on here 
See Me Beautiful - Sizer Hazel
This Kind of Love - Sister Hazel
Smile - Uncle Kracker (this was the song we danced to at our wedding, I love it)
Another Day in Love - TJ McCloud
Always Will Be Yours - TJ McCloud
Lovely Tonight - Joshua Radin
Everything - Michael Buble
Here are a few more (songs that didn’t make the CD, but were contenders):
Fit - Jeremy Lister
You - Michael Warren
I’m Yours - Ron Pope
Rainy Night in Soho - The Pogues
Ocean of Noise by Arcade Fire
Fairytale of New York, The Pogues
“This Life” from the recent “Working on a Dream” album might work.
I was also thinking:
“Harbor” by Vienna Teng
and
“Secret O’ Life” by James Taylor
James Taylor, “Something in the Way She Moves”
And my favorite happy bluegrass love song:
“Till the End of the World Rolls 'Round,” by Flatt and Scruggs, which may not be realistic but it’s filled with joy.
In case all the serious suggestions make you too emotional when you’re listening, you can always throw in Tom Lehrer’s “When You Are Old and Gray.” 
I really should have thought of this one earlier*: Still the One by Orleans
*I know why I didn’t, but I still should have.
Damien Rice – Cannonball. A bit more about falling in love than being in enduring love, but it’s still very pretty.
Foo Fighters is one of the only modern rock bands to write mostly straightforward love songs that aren’t dark. Everlong and Times Like These may satisfy your need for something up-tempo.
A bit depressing, but Naked As We Came by Iron and Wine is a beautiful sentiment.
Geez, Wilbo523…how did you ever find all these oh-so-appropriate suggestions??
mmm
Kind of wondering about Anna Begins on this list. I always thought it was about trying to figure out if you want to have sex with your gal pal or not. I don’t see how it could be a mature, serious love song. More like a fuck song.
But, it came out when I was a teen and I was a gal pal to a lot of guys and trying to decide if I wanted to have sex with them. So, my interpretation may be off. What is your take, Jonathan Chance?
Thread over. This was my wedding song and it still brings me to tears every damned time I hear it.
Also, “The Luckiest” by Ben Folds.
Nick Cave- Into My Arms
Christy Moore- The Voyage- particularly relevant if you have kids.
Metallica- Nothing Else Matters
Joni Mitchell- My Old Man (good if your aren’t married)
Somebody - Depeche Mode