Which song lyrics send shivers down your spine and really hit you emotionally?
Oh, so many.
Can't (Halloween Valentine) by Scarling really gets to me, because I've gone through an experience like that. Another one in that vein is Ampersand by Amanda Palmer, though it was a different experience.
In terms of pure emotion, Strength Through Music and The Point Of It All, both by Amanda Palmer, are particularly heart-wrenching.
Then there's The End Of The Tour by They Might Be Giants, but that's probably due to my own interpretation. :P