Not necessarily about loneliness. Songs that have a lonely feeling or sound to them. The first one I thought of is The Eagles - Take It To The Limit. Always sounded very lonely to me. ( I couldn't find the studio version on YouTube) Are there songes that sound this way or have this feeling for you?
A pair of Peter Rowan tunes (via Old and in the Way) fit the bill: That High Lonesome Sound Lonesome LA Cowboy
Another one by Glen Campbell, "Hey Little One"...the theme of loneliness is one of my favorites in music, although it can be almost too sad in large doses...
Although the song is called Lonely, I think the delivery and the way it is recorded evoke that feeling without even hearing the words. Tom Waits - Lonely
lotta Springsteen's early 80s material- "My Father's House", "Downbound Train", even "The River" (which evokes the worst kind of being lonely, when there's someone right there in the same room with you) R.E.M.'s "Good Advices" "at the end of the day/ when there are no friends/ when there are no lovers/ who are you going to call for" Cream's "As You Said" the sound of a guy sitting in a room trying to piece together where it all went wrong... the Replacements' "Here Comes a Regular" and Westerberg's solo "Sadly Beautiful" (or was this the Mats too, in a hurry right now).
I must be from another planet because none of the songs posted so far make me feel in the least bit lonely. This song on the other hand makes me feel crushingly lonely and beyond desolate inside. And I really like that feeling.
Sinatra's In the Wee Small Hours album. This is the song I'm most familiar with, a master class in singing: "What Is This Thing Called Love?"