I only learned this a week or two ago, when a DJ on SiriusXM mentioned it after playing “Have a Cigar.”
Bjorn and Benny each sang solo lead on a few ABBA songs.
I have a usb thumb drive with about 1500 songs on it plugged into my car audio, usually set to play randomly. One day when I was on the way home from work, it played “Have A Cigar” followed by “Hats Off To (Roy) Harper”. I got a big kick out of that.
That’s a really cool coincidence!
All 5 members of Take That have sung album tracks, although I can’t find a released single that Jason Orange led. Not that I’ve looked very hard.
No one knows who did. 
From wikipedia: The cowbell on “(Don’t Fear) The Reaper” may have been played by Albert Bouchard, David Lucas or Eric Bloom.
They really shouldn’t have let Peter sing.
Phew! I was killin’ myself tryin’ to figure out which song Marc Perlman sings lead.
Ah, file that under my prejudice that drummers don’t really count. They just bang on things, don’t they? 
ETA: another one of my former examples, the original Byrds, were another band where everyone sang but the drummer (Michael Clarke). Later drummers of the band, Kevin Kelley and Gene Parsons, did. I think Michael Clarke is the only member in the Byrds’ history who never sang lead.
Marc plays bass (Jayhawks). And the drummer does sing lead on a couple songs.
Oops, I think I confused Marc Perlman with Tim O’Regan or which instruments they play, respectively.
All the examples I can think of have already been mentioned, with the exception of a few other supergroups a la the Wilburys, which may or may not count. (In many cases, such groups have to be supplemented with other instrumentalists.)
Bands like these (including many of the specific ones mentioned), where all, or at least several, of the members are capable of singing lead, tend to be my favorites. Maybe it’s because it allows for more variety and versatility in their overall catalog, and/or because such bands also tend to be capable of good harmony or backing vocals.
Phil Collins would like a word with you.
Is it Sussudio?
As would Don Henley, Levon Helm, Mickey Dolenz, Ringo Starr, Roger Taylor and that’s basically some from my generation. Plenty of older and younger singing drummers.
Who didn’t really even know how to play the drums prior to the Monkees; he’d been a vocalist in one or more smaller bands prior to then, and had to take drumming lessons in order to be credible in that role with the group.
The producers decided which of the four Monkees would be placed into which musical role, and in every case, it appears that they picked a guy who wasn’t as skilled in that role as another member of the group. Davy Jones was actually a good drummer, but the producers wanted the “teen idol” member of the group to be out front, and Jones (who was maybe 5’ 3" tall) would have been hidden if he’d been behind the drum kit.
According to Peter Tork, if the Monkees had actually been slotted in according to their musical ability, it would have been Dolenz on vocals, Jones on drums, Tork on guitar, and Mike Nesmith on bass.
Word. It’s a testament to their talent and work ethic that they became a pretty good band despite the weird constraints they worked under.
Don’t forget Barry Wom!
En Vogue. They were all lead singers.
With the band KISS ( when he was in the band ), but NOT including his solo album from 1978, nor his solo career.
Shock Me
2000 Man
Hard Times
Rocket Ride
Dark Light
Into the Void
Would The Association count?