Didn’t John Entwhistle sing the Who’s “Boris the Spider” and “My Wife”?
U2’s “Van Diemen’s Land”, sung by The Edge.
“Bridge Over Troubled Water.”
Entwhistle sang on most of his own compositions for the Who.
The Kinks: “Strangers” with Dave Davies as the lead singer.
Allman Brothers: “Hoochie Koochie Man” with Berry Oakley
I’d also nominate Happy for Keith Richards’ vocal.
Kinda surprised I don’t see a mention of “Oh, What a Night (Late December, 1963)” by the Four Seasons, sung by the drummer, not Frankie Valli, except for maybe the bridge…
ETA: Oh, and duh - a song I’ve done in pretty much every band I’ve ever been in - That’s What I Like (About You) by The Romantics - again, sung by the drummer instead of the normal coupla frontman singers…
Borderline, IMHO, in that Art’s vocals are almost as prominent as Paul’sin many (perhaps most) S and G songs. But I think it fits, so, good one! Also, “For Emily, Wherever I May Find Her.”
And, “Living on a Thin Line”.
I was asking myself the same thing, except for “Takin’ Care of Business”. (Randy Bachman is not one of the lead singers of BTO?)
They Might be Giants leads John Linnell and John Flansburgh occasionally let others in front of the microphone including drummer Marty Beller, bass player Danny Weinkauf and Flansburgh’s wife Robin Goldwasser.
Here’s a video fave of mine featuring Weinkauf in the lead.
Oh La La was also sung by Ronnie Lane.
The only song sung by John Cale with VU was Lady Godiva’s Operation. Plus Doug Yule sang a few songs on Loaded.
Carl transitioned into the lead vocalist of the Beach Boys as the 60’s went on. Of course they were a multi-vocalist group and all had more of an opportunity as Brian’s involvement lessened.
One of Be-Bop Deluxe’s best songs, “Rocket Cathedrals”, was written and sung by the bassist, Robert Bryan. I think Bill Nelson sang every other BBD song.
The classic “London Homesick Blues”, on Viva Terlingua! by Jerry Jeff Walker and the Lost Gonzo Band, was written and sung by keyboardist Gary P. Nunn.
He did.
Yes, those are both Mills. Personally I prefer Texarkana.
Love Will Keep Us Alive. Sung by Timothy B. Schmit, bass player for the Eagles. He sings high tenor, which fits this song perfectly.
It was a hard choice. Both excellent songs. And both better than “Superman,” which wasn’t even an R.E.M. original. 
Queen was blessed to have three strong singers in the band.
Brian May sang “'39” (one of my favorite Queen songs), as well as “Good Company”, “She Makes Me (Stormtrooper in Stilettos)”, and “Sail Away Sweet Sister”, among others.
Roger Taylor had a great falsetto voice, and was the singer on “I’m In Love With My Car”, “Drowse”, and “Rock It (Prime Jive)”, among otherse.
“Mote” by Sonic Youth, sung by Lee Ranaldo. One of my favorite songs of theirs.
“Move On Alone” by Jethro Tull, sung by Mick Abrahams
Toto’s “Africa,” sung by keyboardist David Paich. (Lead singer Bobby Kimball is heard prominently in the chorus, though.)
“You’re Gonna Miss Me When I’m Gone” by Brooks & Dunn, sung by Kix Brooks.