I thought of “More Fool Me,” but figured it DIDN’T count.
“It’s Just that Simple” by **Wilco **is sung by bassist John Stirratt and I think it’s quite good.
I was going to nominate Dan Hartman of the Edgar Winter Group, but, IIRC, he sang almost all of the songs on “They Only Come Out at Night” album.
Gotta confess I’d never heard that song.
It IS better than “Mother”…which is not a lot to say.
I’m glad you didn’t say “Back In The New York Groove” by Ace.
I also like “Wearing The Inside Out” with Rick Wright on vocals. It’s hard to explain because his voice isn’t great. It’s like he’s not singing, he’s telling a story.
If you don’t count The Gift, off White Light/White Heat, although that is more of a spoken word narration than actual singing. He has such a lovely soothing speaking voice, though.
I love The Gift but it isn’t sining. It makes you want to hear Cale narrate a whole O Henry anthology over feedback and drone 
I thought of these three songs right away
Roger Taylor is probably my 2nd favorite vocalist behind Freddie,while I enjoyed the Queen + PR stuff, I wish Roger would have done the vocals himself.
“Numb” was even better.
“Stay” is another that he sings. As you say, his voice isn’t great but it’s pleasant enough, good in small doses and significantly better than Ringo Starr.
I’m not sure if “One of these Days” counts or not. The only line it has is spoken by Nick Mason. I think it may be his only line in the band’s history.
Hell, I sound better than Ringo Starr and I sing like a crow.
“Fun In Space” is one of my favorite albums. I also like his cover of “Racing In the Streets”
I came to add “Hard Luck Woman”, also sung by Peter Criss
Semisonic’s song “In Another Life” is sung by bass player John Munson (not lead singer Dan Wilson). It’s not a bad song, but not IMO as impressive a vocal performance as some of his lead vocals for their previous band Trip Shakespeare (like “Late” and “Lulu”). Those probably don’t count, however, as that was more of a “multiple lead singers” situation.
Madness had some good songs not sung by the regular lead singer, including “Tears You Can’t Hide” and “Michael Caine” sung by Cathal Smythe and “Razor Blade Alley” sung by saxophonist Lee Thompson.
One of my favorite Men At Work songs is “Giving Up,” sung by the late Greg Ham.
Does Your Mother Know? - ABBA
Not sung by Agnetha or Anni-Frid but by guitarrist Björn Ulvaeus.
Gotta go with “Tempted” by Squeeze, the only lead vocal from Paul Carrack, their keyboardist for one album. It’s probably their best known song in the US.
If the OP hadn’t specified great songs, I’d mention “How Many Say I”, the only Van Halen song to feature lead vocals from Eddie Van Halen.
“Wart Hog” by Ramones featured a vocal from Dee Dee.
I see I’ve already been scooped on the Dave Davies contributions to the Kinks’ repertoire.
Sand Storm by Bitter Destiny, sung by the bassist Anthony “What?” Gilbertson.
Good call, but a nitpick: Carrack also sang lead on “Loving You Tonight,” a single from Some Fantastic Place, released in 1993. Twelve year gap between “Tempted” and this one. Not as famous as the earlier track, but still a damn good one.
If we’re talking Squeeze, I’m going to nominate “Cool for Cats,” sung by lyricist but background vocalist Chris Difford. One of their biggest hits, #2 in 1979.
One of my favorite Toad the Wet Sprocket songs is “Crazy Life,” sung by guitarist and background vocalist Todd Nichols (Glen Phillips is the lead singer).
The best song, IMO, on The Jacksons’ Victory album is “Wait,” sung by Jackie Jackson (Michael sings ad libs at the end of the song). “Body,” sung by Marlon, was a single from the record.
Great song. Up until Dark Side Of The Moon, Wright was pretty much one of three lead vocalists for Pink Floyd, including singing on some of the early singles. If we’re counting him as an occasional vocalist, “Remember A Day” is my contribution for this thread.
He also sang joint lead with Gilmour on some of his recent solo tours, and the version of “Comfortably Numb” from Live In Gdansk is probably my favourite version of it, with Wright doing the vocal part Waters did on the original.
If you like “Wearing The Inside Out”, it might be worth checking out Wright’s solo album Broken China. It’s not the most cheerful of albums, but has a somewhat similar feel to that song.