Not sure if this has been done, but searched and didn't find any topic focusing on this subject.
I was thinking about progressive songs that becomes very emotional. Not talking about songs that are just focusing on being emotional, but songs that connect and becomes emotional for you! Also they need to have progressive qualities so songs like Hollow Years, Which You Were Here etc. don't quite fit.
This is a bit of a vague definition and there will be songs that are hard to say if they are "progressive" or not. But I found that most emotional songs by example Dream Theater don't fit my definition of progressive pieces. The Best of Times and A Change of Season certainly fits but Vacant, Disappear (this is a cloooose one), Far From Heaven doesn't imo. They need to have a certain music complexity to them which makes the list a bit harder.
My quite short list of songs I could think of are (in no specific order):
Dream Theater - A Change of Seasons
Let's get this one out of the way. Once I understood the subject of this song it's always been a very emotional ride. Such a brilliant piece of music with strong lyrics and heart-gripping story. Carpe Diem and Another World is just so beautiful written and sung.
Pain of Salvation - Beyond the Pale
Pain of Salvation often focus on strong emotions in their music and this is one of the highlights. That song is a sledgehammer. It get's me every single time. The music sets the emotions right of and Daniels singing is unbelievable!
Pain of Salvation - Nihil Morari
What a song. Not sure why this one isn't talked about more often. Great music and the finishing lines brings a tear to my eyes every single time.
"I'm sorry!
For the things we did and didn't do
Forgive us; the fools that rushed ahead without a single clue
... Without a single clue ..."
Pain of Salvation - Rope Ends
Another PoS track (I could include so many but will stop here). This one has a very clear story and is told in such a masterful way. The way Daniel delivers the pure agony of the story is amazing. The double vocal chorus is one of the most beautiful written music I know.
Pink Floyd - Shine on You Crazy Diamond
A classic that doesn't need much introduction. The guitar, the singing, the subject. All emotions are delivered just perfectly on this one.
Cult of Luna - Dark City, Dead Man
Actually haven't given much though about the lyrics but the music is enough. The way the song just builds for that final big dark ending is music history. It hits me emotionally on a music level.
Everygrey - When The Walls Go Down
A strange one to have on the list but well deserved. David Wilkerson's speech "A Call To Anguish" is played in background accompanied by the band. A very cool idea that also becomes very emotional thanks to the emotions from the speech and music from the band.
Anna Von Hausswolff - Deathbed (bonus)
This is maybe a grey zone of "progressive", but damn it's amazing. The music changes and progress in a very emotional way that just becomes bigger and bigger for each minute. Not much singing but the few lines (and the title I guess) in there explains the emotional subject at hand.