I'm sure I have a lot, but comes to mind:

EDIT: Sorry this turned into a big reply haha...

• Zombie (both the original and the 2016 Bad Wolves cover) , the second it opens, just visceral; it's the same old thing, in [2026], in our heads...
• The Kids Aren't Alright by The Offspring , I hate relating so hard to this as a generation, watching so many kids with promise just get smothered out surviving in a bleak "cruelest dream reality." Oft by drugs and hopelessness.
• In the Arms of an Angel by Sarah McLachlan : My mom always cries if she hears this song because her late mom did too. Then my cousin sang it at my dad's funeral so...Yeah, I don't let that one play. Sorry, Sarah.
• Immortal by Marina and the Diamonds ; The entire song is beautiful and profound. "And if the earth ends in fire, and the seas are frozen in time, there'll be just one survivor, the memory that I was yours and you were mine." (Holy shit just typing that...)
• Pretty When I Cry by Silent Rival ; Such a beautiful song I thought was about a partner who taught the singer about true unconditional love... It's about her late mother. It empowers me to fight to be there for those I love, and it sends a powerful message that we can be strong in our weakness.
• Dust in the Wind by Kansas ; anything about the fleetingness of life hits me hard.
• Memories by Maroon 5. I miss people...

Lots of happy songs too...Like they're beautiful and wistful and lovely and I think I cry because I can't imagine such peace... My wife likes these songs and I guess I kinda break imagining us getting to just unshoulder our burdens and truly live.

• Perfect by Ed Sheeran
• Just Too Good by Phil Wickham
• "Will the Circle Be Unbroken?" , a popular Christian hymn from 1907, made prominent in recent history by BioShock Infinite.
• On that note, Amazing Grace really is amazing, but it doesn't help that it's the 'somebody died' song now...
• The Prayer by many artists: Celine Dion and Andre Bocelli
• Prayer by Hayley Westenra
• In My Arms by Plumb (has some sweet remixes, but man, a mother's love is truly something...our first is on the way and I really feel it now...)
• Somewhere Only We Know by Lily Allen

... Okay I'm sensing a theme here. Yeah, I'm a person of faith. Thinking of a refuge in my Father where I can stop worrying, stop fearing, stop fighting. Songs about pure and unyielding love, or lullabies , crush me instead of relax me for some reason. Maybe because the contrast with our present circumstances is so harshly defined and such respite feels like it can't be had in this life.