I see some rock songs posted. This one, the album track never got me, but i saw a live performance on TV and for some reason that one got me close, maybe it was the crowd's reaction. I won't forget the crowd waited in silence until she stopped completely and there was this short bit of total silence before they erupted. Between the song itself and the theme it is based on and the total respect the crowd had for her performance it got me close. I forget what it was on, letterman or SNL or something in the 90's. Can;t find a recording of it now of course, but here is the original music video, not the same without the crowd reaction. Note, the first half of the song is not what I am talking about, it is the second half. One of the very very few modern performances that stuck with me because of the thread topic...
Otherwise very little pop/country/rock will get me feeling like that, usually it has more to do with the words and some meaning personally in my life then the song itself. I can be moved by a few various classical music pieces, but not the stereotypical ones everyone thinks of. A lot of that is personal experiences also. A simple example is one of the tracks from Patrick Cassidy's Dierdre of Sorrows has two female vocalists that take turns singing. The second, is a dead ringer for my Mother's voice as I remember it from my youth sitting next to her in church every Sunday and listening to her practice in the choir(it was 7 people in the choir, we lived in a tiny town) before we went either to the grocery or home. It isn't the song or especially the lyrics, it is the voice of the vocalist.
That is how many pieces of music can make me emotional, it is life experiences tied to them or other personal things that will take it to my heart. The few more "pop song" type songs have a serious undertone, like the Edmund Fitzgerald where the event the song is about are tragic enough to inspire emotion in me.
Someone mentioned TAPS in this thread. As a kid I got the respect vibes from it. After the first funeral I attended where the local vets came and played and did a salute, can't listen to it played live even once without choking up. The meaning embedded in that short simple piece is mountainous.
Now then, that is enough touchy feely for a while!