A lot of the music that affects me is music, no words like the Gary Moore instrumental version of "The Messiah Will Come Again" by Roy Buchanan, "Suspension" by Jeff Beck, "The Ballad of Bill Hubbard" by Roger Waters, along with classical music like Barbers "Adagio" and in particular Henryck Gorecki's "Symphony of Sorrowful Songs".
Most songs are specific to a moment in time, a period of emotional turbelance, be it good or bad. For me a song by a Japanese multi-instrumentalist, Kitaro, called "Lady of Dreams" with lyrics by Jon Anderson of Yes is one such song. It is particularly difficult for me to listen to as the words seem to echo so accurately my feelings for an ex-girlfriend. The songs get hotwired, burnt into the brain during such emotional highs and lows.
Others are more cerebral such as "Sugar Mice" by Marillion that reminds me of my father. Some are so strangely compelling that they move you even if you're not sure why, such as Johnny Cash's "Hurt".
It's all pretty subjective, we all react differently, but no one is immune.