Check out
Jim Offerman! 
I don't listen to most pop music, but my sons do. I'm often surprised by the wisdom and feeling of some of the songs - there IS some good stuff out there.
I also go see local singer/songwriters - their stuff is generally not on the radio, but it is often heartfelt and moving. I listen to
WNCW (you can listen online) during the week - they play many independent singers and bands. That's where I first heard
Toubab Krewe and
Madeleine Peyroux. They have a different playlist on the weekends.
Like chermille said, sometimes a song that's about heartbreak or new love or whatever just resonates, 'cause that's where you are... like Jackson Browne's "
Everywhere I Go" (click on that title) - he's not really saying anything new, but if you hear that song when you're falling in love... he caught it. He caught that feeling perfectly. It's a combination of lyrics, rhythm, tone...