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".
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".
The title track. It's about a man going up into one of the towers to rescue trapped people, and the gorgeous melody just adds to it.
Some someone who lives in New York City, "City of Ruins" can be a very powerful tearjerker..
On the 2012 tour, Bruce uses this song to introduce the band. After he introduced everybody at the show this troper saw, he asked "Are we missing anybody?" He didn't need to mention Clarence Clemons' name; 65,000 people held up their hands and bowed towards the stage.
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.
"Brilliant Disguise", about a married couple who stopped loving each other.
"Highway Patrolman". It hits even 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 Heavens' 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.
"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
This troper thinks "Johnny 99" is one of Springsteen's most depressing. The absolute despair in the song is tear-worthy every time.
Shut Out the Light is an absolutely heartwrenching song about PTSD. While the protagonist of the song returned from the war alive, he is so broken, he could just as well be dead. Never fails to bring this troper to tears.
"My Father's House" : the narrator has a dream about reuniting with his estranged father. He awakes and rushes out to his father's house to repair the rift between them.
I walked up the steps and stood on the porch A woman I didn't recognize came and spoke to me through a chained door I told her my story and who I'd come for She said "I'm sorry, son, but no one by that name lives here anymore"
"The Wall" from 2014's High Hopes. The narrator visits the Vietnam Memorial to pay tribute to a good friend and fellow musician; it's been years since his friend died in the war, but he's still heartbroken and angry about the loss and the general futility of the war.