Probably too many to mention, but two I can't sing and play along to without crying would be For No One - The Beatles, and '39 - Queen ....heartbreakersFor me, two stand out: "He Stopped Loving Her Today" by George Jones and "Back on the Chain Gang" by The Pretenders.
Which songs "really get to you"?
"It Makes No Difference" - The Band (This version below). When Danko gets to the part "Well, I love you so much. It's all I can do" it's instant goosebumps and misty eyes. Not sure why, his voice and the song just hit me.
Hello In There is one that gets me. So much truth in that song