The Rose - Bette Midler (This one has always stood out to me; probably my pick for the most beautiful song ever.)
Somewhere Over the Rainbow - Israel Kamakawiwo'ole (No disrespect to the wonderful Judy Garland, but this version kills me every time. Kills me I tell you.)
Today - Jefferson Airplane
Comin' Back To Me - Jefferson Airplane ("The summer had inhaled and held its breath too long." One of the greatest opening lines ever.)
God Only Knows - The Beach Boys
All I Want Is You - U2
I Love You - Sarah McLachlan
Moonshadow - Cat Stevens
Hallelujah - Jeff Buckley
Con Te Partiro - Andrea Bocelli and Sarah Brightman
The Beautiful Ones - Prince (though I first fell in love with Mariah Carey's cover *flinches*)
Unforgettable - Natalie and Nat King Cole
More Than This - Roxy Music
The Scientist - Coldplay
Fix You - Coldplay
Collide - Howie Day
Waterloo Sunset - The Kinks
Just The Way You Are - Billy Joel
She's Always A Woman - Billy Joel
Lightning Crashes - Live
In My Life - The Beatles
Tiny Dancer - Elton John (I'm not sure if beautiful is the word for this one, but if not, it's very close)
Your Song - Elton John
A Little Ray of Sunshine - Axiom
Because I Love You - Masters Apprentices (Still not crazy on the chorus, but the verses are exquisite.)
Mr Bojangles - Harry Nilsson
This Woman's Work - Kate Bush
Tenterfield Saddler - Peter Allen
Walking After You - The Foo Fighters
You Belong to Me - Vonda Shephard and Tori Amos get my top votes, but the song is beautiful regardless of who sings it.
And to wrap-up with the FM ones...
Crystal;
Sara;
Landslide;
Songbird;
Storms;
Beautiful Child;
Dragonfly