Truly, Madly, Deeply by Savage Garden became the theme song of our first road trip in the US in spring 1998 that convinced us to move here. It was high in the charts and played very frequently on the radio as we drove around the southwestern US (we drove from Phoenix to SF through lots of national parks). I particularly remember it playing as we drove to Monument Valley so it brings back memories of standing on the hill at the visitor center and admiring the vista (with the appropriate words in the chorus!). We had to play it again when we went back with the kids nearly 20 years later…
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A few that come to mind. But for me there are POSITIVE impact songs and NEGATIVE impact songs - they both elicit a strong feeling!
Negative:
What A Wonderful World
Somewhere Over The Rainbow
Cats In The Cradle
Tears In Heaven (Eric Clapton) - this one is sooooo sad
Positive:
September (Earth Wind and Fire) playing football in college
Any song from the Parent Trap soundtrack (our family’s fav movie) I’ll laugh AND cry!
Jumpin Jack Flash, Tumbling Dice, etc. (Rolling Stones) Dancing on our desks in college 
Two Princes (Spin Doctors) Possibly my all time fav song and a song I would dance with my kids to when they were little AND may be odd, but the BEST memory, the song I danced with my son to at his wedding!!
A Sky Full of Stars (Coldplay)
And finally the unexpected, but for personal reasons it makes me both happy and chokes me up…
Oh, Canada 
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I feel the same way, @abasket, when I hear any of the armed forces anthems (especially when our son was in uniform on the parade field while the Army song was playing–huge, huge tears):
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The big one for me. The living years sung by the great Paul Carrack as part of Mike and the Mechanics
And the last resort. Don Henley tries to write meaningful stuff.
Everybody has a dream and get it right the first time. Billy Joel
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Just for kicks I created a song list of all your impactful songs while lazing around, drinking my coffee this morning. Even Oh, Canada because why not!?
I need to give some thought to my most impactful songs. There are different ones from different times of my life. And as someone else said, some evoke a more positive reaction than others but are still impactful.
One I will throw out that almost hurts every time I hear it because it reminds me of a time I was living far away from a loved one…
Set the Fire to the Third Bar by Snow Patrol
ETA: and yes, I included @Catcherinthetoast’s stellar suggestions from that infamous summer at band camp.
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I have many. These take the lead.
-What a Wonderful World by Louis Armstrong
-Imagine by John Lennon
- Vincent by Don McLean
- House of the Rising Sun by The Animals
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“House at Pooh Corner” - always reminds me of when S was little and I used to sing it to him. During the pandemic when he was on lockdown in London it was painful for me to hear.
On a happier note hearing “Dancing Queen” (I’m a big ABBA fan) takes me right back to being in college and attending fraternity/sorority formals - oh to be young again!
So many others…
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Dan Fogelberg’s Leader of the Band, a tribute to his father who was a high school music teacher.
The leader of the band is tired
And his eyes are growing old
But his blood runs through
My instrument
And his song is in my soul –
My life has been a poor attempt
To imitate the man
I’m just a living legacy
To the leader of the band.
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There are sad songs from specific times, but I actually don’t like to think of them because they make, well, sad. Harvest Moon by Neil Young makes me wail, even though I love it. In fact, I have to turn it off right now. It was one of my mom’s favorites. Still too recent to think about just happy memories of her.
So I prefer to think of songs that I have associated with happy times in my life.
I’ll add Hey Ya by Outkast. I can’t hear this song and not dance. It reminds me of so many fun parties and gatherings we’ve had since we moved to the Northeast in the early 2000’s, when it was playing at every party, bbq, and bar/bat mitzvah. I love the video too.
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This from the Fab Four on the David Frost’s Frost on Sunday show from 1968. Timeless:
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I love Hey Ya also, but was surprised to find out years after it was released that the lyrics aren’t happy at all. I just listened for the beat, never really heard what the lyrics were saying.
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Well, I suppose the guy singing is pretty happy, haha. At least he’s “just being honest.”
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“Ohio” by Crosby Stills and Nash.
Brings me right back to high school when the draft and Vietnam made the world look bleak. Draft ended just before I became eligible. Carried that draft card in my wallet until it literally fell apart.
The breakdown in our society today reminds me so much of those days. Pro-war and anti-war factions. Conservatives calling anti-war protesters bums and traitors. Out-there left calling the police pigs. Tumultuous times.
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That would be a very long list since I love music and it tends to evoke strong emotions. One song that comes to mind though is Praise you in the Storm by Casting Crowns. That song got me through so many hard times near the end of my marriage when things got really bad and during the divorce and the period following that. I still will almost always break down crying when I listen to it, but it also cuts through the routine, softens my heart and brings me to a place of worship, so it is definitely a positive.
A song that makes me laugh because of a memory associated with it is Hey Jude. When my youngest son was around 3 or so we were going somewhere and I was playing music and singing along when he started crying. He was of course in the back seat in his carseat and I had no idea what was wrong so I quickly found a place to pull over so I could check on him. I was trying to calm him down and ask what was wrong and he said “you said hate you”. Instead of Hey Jude, he thought I was saying hate you and he was so upset that he was hysterical. After a few minutes of explaining and comforting him we were back on our way.
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Piece by Piece - Kelly Clarkson
Cannot listen while driving, have to turn it off before I start bawling.
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California Dreaming
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What’s a 45? Is that the thing shown here?
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You actually know the Flintstones?
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Gordon Lightfoot - Beautiful
Bread - Make It With You
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Songs that transport me to different times (living in Spain, college, parent passing away, etc)
Hey Brother by Avicci
Hotel California
J’ai Cherche (Amir)
Sultans of Swing
Layla
Cruz de Navajas (Mecano)
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