Ryan,
If I understand correctly, I think you are referring to songs which elicit a strong emotional response, songs that are cathartic in nature as opposed to just "sad". I'm only saying this because the Jurassic Park theme, for me, moves from sadness to a sense of joy as the theme concludes. If I'm wrong, please ignore this post. If I'm correct, you may want to listen to this short movement from Will Todd's "Ode to a Nightingale" (a musical setting of John Keats' poem by the same name). Start at 1:55 and listen for 2 minutes. This doesn't make me sad, but it does often reduce me to tears.
I love music like this, music that takes you for an emotional journey and cleanses the soul. The entire work is around 35 minutes in length and takes you on a roller coaster ride of emotions.......worth at least a 2 minute listen.