Not many obscure ones, but these still will stop me in my tracks:
"The Flat Earth" - Thomas Dolby
"Saved By Zero" - The Fixx
"The Wreck of The Edmund Fitzgerald" - Gordon Lightfoot
"Fire and Rain" - James Taylor
"Head Over Heals/Broken" - Tears for Fears
"Wouldn't It Be Good" - Nick Kershaw
"Dust In The Wind" - Kansas
"Take It To The Limit" - The Eagles
"Family Snapshot" - Peter Gabriel
"Main Street" - Bob Seger
"Solsbury Hill" - Peter Gabriel
"It's For You..." - Pat Metheny Group
"Skateaway" - Dire Straits
"Meeting Across The River" - Bruce Springsteen
"Mad World" - Gary Jules (Truly one of the saddest songs ever performed)
I hadn't thought of Skateaway in so long, but that's definitely a song that stops me in my tracks.
Also on my list:
At 17 by Janis Ian
Coming Up Close by Aimee Mann
Don't Let it Bring You Down by Neil Young