He won’t sing songs like that anymore, though. During concerts, he says that the only four-letter word he’ll say now is Love. While he was always a little bit religious, like with the aforementioned songs, the last few years have found him a very devout JW. He even goes knocking on people’s doors to spread the word. (Wouldn’t you just DIE?) His last album 3121 is quite religious but still rocks.
In My Life is a secular song. However, it is one of the very rare secular songs I’ve ever heard in church.
Just Another Poor Boy by Chris De Burgh
Drop Kick Me Jesus Through The Goalposts Of Life by Bobby Bare
A lot of reggae.
Forever Loving Jah by Bob Marley
Speaking of JW, if I understand correctly, Stevie Wonder wrote “Spiritual Walkers” in defense of the Jehovah’s Witnesses, although Stevie himself is not a JW.
Other Stevie Wonder songs on religious themes include “Have a Talk with God” and “Heaven Is Ten Zillion Light Years Away.”
U2’s the first band that came to mind after reading the OP. Their “How to Dismantle an Atomic Bomb” is (IIRC) comprised entirely of religious-themed songs.
Nick Cave has a number of 'em – the first that comes to mind is “Into My Arms.” Along that line, PJ Harvey (about whom “Into My Arms” was written, IIRC) also refers to religion in a bunch of her songs (like “The Garden,” “Long Snake Moan,” “Send His Love to Me,” etc).
The Waterboys’ “Glastonbury Song” is spiritual and has a great chorus: “I just found God…where He always was.”
Cold War Kids’ “God, Make Up Your Mind”
Morrissey’s “I Have Forgiven Jesus”
Mule’s “I’m Hell”
Depeche Mode’s “Personal Jesus.”
All of 16 Horsepower’s songs are explicitly about religion, and they could be classified as blue-grass, but they’ve got a wild-eyed, occasionally frightening (in the best possible way) vibe that would keep them from being “typical” religious music.
And there’s always Type O Negative’s “Christian Woman,” but I don’t know if that’s what the OP was looking for. 
“All You Zombies” by the Hooters
“Flood” by Jars of Clay
“Personal Jesus” by Depeche Mode (later covered by Johnny Cash and Marilyn Manson*)
*Seperately - but wouldn’t it have made a cool duet
Well, there’s a fair chunk of Nick Cave’s output.
Wormwood by the Residents is a concept album about some of the more interesting bits of the Bible.
I fell in love with this song before I found out it was by a Christian band. (Not that there’s anything wrong with that, I just probably would have avoided it.) I like JoC, and they have an acoustic and electric version of the song.
One Toke over the Line…Sweet Jesus…One Toke over the Line…Brewer and Shipley
,
tsfr
“Jesus is just alright” and “Turn!turn!turn!” both by the Byrds
“Dimming of the Day” by Richard & Linda Thompson, by Emmylou Harris, by the Five Blind Boys of Alabama
“Shake a hand” by faye Adams
“Touch a hand” and “I’ll take you there” by the Staple Singers
“His eye is on the Sparrow” by Lauren Hill and by Selah
“Beneath still Waters” by Emmylou Harris
“Oh! happy day” by the Edwin Hawkins Singers
The Goldberg Variations, by Glen Gould…
seek out his last recording of the Bach clasic
Or admit you do not have a soul
FML
“Jesus Christ Was Born Today” by Alex Chilton/Big Star.
“Spirit in the Sky” would show up on the oldies station.
Never been a sinner, I’ve never sinned
I’ve got a friend in Jesus
So you know that when I die
He’s gonna set me up with the spirit in the sky
but I’m starting to think it was tongue in cheek.
One of the members of JoC and his family are acquaintences of mine - we attend church together. Very nice family with cute young boys. Nothing more to add, just wanted to share my brush with semi-fame 
Give Us a Song by Jonathan Edwards is lovely, if you can dig it up.
Bob Dylan’s Slow Train album. It’s an all-Christian compilation.
This is the first (and, if I understand correctly, most highly regarded) of the three albums cbawlmer mentioned in Post #17.
I rather enjoyed the Kentucky Headhunters cover of the song. They changed the first two lines above to
I’ve been a sinner, yes I’ve sinned,
But I’ve got a friend in Jesus
I thought it made a marked improvement in the song.
I liked this song so much when I first heard it, that even after I found out they were a Christian band, I went out and bought the CD, and actually like the whole thing. And I’m Jewish! :eek: