Bruce Springsteen/Tear Jerker

This heartland rocker can move people to tears, whether or not they live in New Jersey.

"Devil's Arcade".
Also, "Streets of Philadelphia". "The night has fallen/I'm lyin'awake/I can feel myself fading away/So receive me, brother, with your faithless kiss, or will we leave each other alone like this/On the streets of Philadelphia..."
As well as "Atlantic City", especially the line 'Maybe everything that dies one day comes back'.
Gotta give some points to "The River", which probably single-handedly earned him the nickname of "John Steinbeck in black leather".
Then there is "Devils and Dust". The video is especially powerful.
Along with "Lonesome Day". For all that it sounds like a rousing anthem, it's actually from the POV of the relatives of those who died in 9/11.
The album The Rising can utterly wreck anyone who was touched by 9/11. Particular mention goes to "Empty Sky" -- particularly the lyric "I want a kiss from your lips, I want an eye for an eye... I woke up this morning to the empty sky..."
- Not to mention "Into The Fire" and "You're Missing".
Some someone who lives in New York City, "City of Ruins" can be a very powerful tearjerker..
A live version of "4th of July, Asbury Park (Sandy)" performed right after the death of E Street member Danny Federici. Right before they start the song, Bruce says, "We'd better get this right...someone's watching."
- On a related note, "The Last Carnival" was written as a tribute to Federici. "We'll be riding the train without you tonight/the train that keeps on moving, its black smoke scorching the evening sky/a million stars shining above us like every soul living and dead/has been gathered together by God to sing a hymn over your bones..." It's even more poignant if you know that Federici's son Jason plays the accordion in the song.
"Born in the USA", which is about the treatment of the Vietnam War soldiers upon returning to America.
"My Hometown" - complete with It Got Worse and Downer Ending.
"Cover Me" is actually a pretty lively song which, if you're in the right mood, could be cheerful. However, those who are a state of depression may interpret the lyrics as a request for assisted suicide. It would not help.
The album version of "No Surrender" seems to be a generic rebellion song. The live version, however, sounds a whole lot like an elegy.
41 Shots (American Skin.) Wow. Doubles as Crowning Music of Awesome.
"Highway Patrolman" It hits harder if you've seen the movie that Sean Penn made based on the song, The Indian Runner
"Youngstown" - a powerful story of not just death of an industrial town, but the whole steel industry in USA, and the collapse of the American working class and their dreams. The final words, said by the mouth of an old steelworker, are true tear-jerkers:

When I die I want no part of Heaven; I would not do the Heaven's work well
I pray the Devil to take me to stand at the fiery furnaces of Hell

"Gypsy Biker," about the narrator's brother being killed in Iraq.
"Bobby Jean." When he says that he wants to say "I miss you baby, good luck goodbye, Bobby Jean..." not crying isn't an option.
"Downbound Train." The Downer Ending is sad as all hell.
May be YMMV but "Wreck On The Highway" is a tearjerker song in which the narrator finds the victim of a car crash, who presumably died right in front of him after pleading for help. After watching the man carted away to a hospital the narrator delivers the saddest line of the song:

I thought of a girlfriend, or a young wife, and a state trooper knocking in the middle of the night
To say your baby died in a wreck on the highway

Another YMMV but this troper thinks Johnny 99 is one of Springsteen's most depressing. The absolute despair in the song is tear-worthy every time.
Now, YMMV, but anytime that sax comes on after Clarence Clemon's passing, this troper gets a little teary.