I’m tempted to offer “Atheists Don’t Have No Songs”
The serious answer is “How Great Thou Art”. Poor recording quality (looks like maybe a hand held iPhone), but I like IIIrd Tyme Out’s version.
I always like
Amazing Grace (my wife doesn’t care for it, though)
Just As I Am, Without One Plea
How Great Thou Art
Battle Hymn of the Republic
Silent Night
Beautiful Savior
A Mighty Fortress Is Our God
The Navy Hymn - Eternal Father, Strong to Save (For Those In Peril on the Sea)
my top four are
- Be Thou My Vision
- O How I Love Jesus
- Amazing Grace
- Turn Your Eyes Upon Jesus
grew up in the Baptist church. Turn Your Eyes was the song they played when the Pastor invited people to come forward for Baptism or to join the church.
I used to love Will the Circle be Unbroken. That’s changed as my mom reached her eighties. If you’re familiar with the lyrics you know why that song doesn’t appeal to me anymore.
Picking a favorite hymn would be like picking a favorite child - it’s impossible. The ones that come off the top of my head:
Praise My Soul the King of Heaven
The King of Love my Shepard Is
Drop, Drop Slow Tears
Be Thou My Vision
Eternal Father Strong to Save
My congregation sings 4-5 hymns every week and there is always at least one that makes me nudge my wife and say “I love this one!”
ETA: Is May the Circle be Unbroken really a hymn? I always think of it as a gospel song. I don’t think I’ve ever seen it in a hymnal, but I hear it on the Grand Ole Opry all the time. 
“I Bind Unto Myself Today” aka St. Patrick’s Breastplate
I grew up in the 70s too and love all those songs. My best childhood friend died when we were 20 (~1987) and they were featured in his funeral, particularly On Eagle’s Wings.
As far as content, Aquinas’s Adoro Te Devote can’t be beat.
Amazing Grace and And Can It Be for me. Dunno if it counts but I like Were You There? when sung acapella (it’s an African Spiritual style).
I dislike A Mighty Fortress.
I love that one!
I love that one!
See what I mean?
There are two sets of lyrics. The original was a hymn. The later one has the mother references.
Blasphemy!
Were You There is a good one. Solemn, somber. I’ll vote for that also.
Sorry! I was fairly surprised at how popular it is here. I’m not quite sure why I dislike it; it sort of makes me think of stuffy, stale churches.
Praise God from Whom All Blessing Flow.
“Built On The Rock” from the Presbyterian hymnal. Never seen it anywhere else.
A running joke in the Navy for the entire 23 years of my service was:
“Let’s sing him the Navy Hymn: (everyone responds) Him, him. . .fuck him!”
Usually reserved for superiors who made poor decisions.
I now return you to your more respectful Dopers.
Wikipedia says yes. The other set of lyrics jsgoddess refers to is properly called Can The Circle Be Unbroken.
I grew up in a southern baptist church family. Most of the songs I liked had different renditions from choir to choir. My favorites are probably Sam Cooke and the Soul Stirrers.
Touch the hem of his garment
Wade in the water
Heavy load
eta: I’m atheist but I think good music is good music.
My favorites are as follows:
Jesus Christ is Risen Today (for Easter)
One version of Psalm 119
Angels We Have Heard on High (Christmas)
Silent Night (Christmas)
Amazing Grace (they can play this at this heathen’s funeral)
Ode to Joy (I love performing this on a church organ)
I grew up RC in the sixties and seventies, but have served as an organist-for-hire in protestant churches over the years and in choirs in the RC and Unitarian churches. While I don’t believe, some of the music is lovely.
After Be Thou My Vision, it’s We Gather Together.
And Silent Night and O Little Town of Bethlehem, American version.