Doobie Brothers, Grateful Dead (both of those bands also had two drummers), and The Rolling Stones (Keith sang occasionally).
Let’s see. I’m probably going to get mercifully mocked for some of these, but…
Phish
Spin Doctors
Mothers of Invention/any Zappa amalgamation
Blood, Sweat & Tears (?)
Did RVZ sing all of Lynyrd Skynyrd’s songs? Sometimes it sounds like someone different. Maybe it’s Johnny. I don’t know these things.
And of course, that should be “mercilessly”, and “while he was alive”. Good day.
I don’t think there’s any “maybe” about the Who. All four members of the Who sang. Well, it may be overgenerous to call what Keith Moon did “singing”, but he did do it on “Bell Boy”, a couple of early Who songs, and parts of Tommy. John Entwistle sang the songs he wrote for the band (most famously “Heaven and Hell” and “My Wife”), and Pete Townshend sang a couple of songs on almost every Who album.
Has anyone mentioned Queen yet? They all sang too.
Sonic Youth
I think KISS probably holds the record in this department, with all four original members doing regular lead vocals (when the original four are together). On their first album there was even a song where three of them each sang a verse. The drummer (Peter Criss) and lead guitarist (Ace Frehley) usually got one or two songs per album, with the remainder being split evenly between Gene Simmons (bass) and Paul Stanley (frontman and rythem guitar). Pretty much the same ratio live. Of nine all time members, only two never sang lead, and neither of them were in the band much more than a year.
Let’s see, X and Sonic Youth have been mentioned…
The Swans
and The Resisdents, come to think of it.
Oh, I can’t believe I forgot one of my favorite bands…! The Ziggens have two singers. 
Didn’t the Beach Boys share vocals? Chicago?
The Bay City Rollers shared vocals, I know. (Go ahead, make fun of me, but I LOVED them.) 
So did the B-52s on occasion.
All I can think of for now.
Sheri
The Cars had Ric Ocasek and that guy who sung lead vocals on Drive. (can’t remember his name)
Squeeze used Glen Tilbrook, Paul Carrack (while he was with the band) and Chris Difford as lead vocalists.
Benjamin Orr.
That would be the now deceased Benjamin Orr.
The only band I can think of that hasn’t been mentioned is Velocity Girl. Most songs were sung by the actual girl in the band, Sarah, but several per album would be done by one of the guys who’s name escapes me.
And I think it’s fair to say that the more Black Francis pushed Kim Deal away from the mike the less interesting the Pixies got. But she only had a handfull of songs where she was the lead vocalist, so I don’t think it really counts in this thread.
God, I can’t believe you people are missing this obvious one:
Queen
Sure, Freddie got all the ink. But all four of them wrote songs and three of them sang. Usually on each album. John Deacon never sang lead on his songs because he never liked singing.
Bassists, they’re wacky.
Or I could send a shout out to New Orleans own, Cowboy Mouth. Fred, John, Paul and Rob all sing lead on the songs they write. They all have different styles and they serve each other well.
Wow. It always surprises me when someone mentions the VGirl. I roomed with Brian for two years back in school.
You just made my day.
Supertramp alternated vocals between Rick Davies and Roger Hodgson.
When Gregg Rolie was still with Journey, he and Steve Perry traded vocals on a number of songs.
Mick Jones of Foreigner took the lead vocal on a handful of songs, instead of Lou Gramm.
The OTHER Mick Jones, of the Clash shared vocals with Joe Strummer.
Everybody in Utopia sings.
XTC has Andy Partridge and Colin Moulding.
There are undoubtedly others…
Chris W
Lacuna Coil
I’m not positive on any of these, but:
Heart (Ann and Nancy both sing, right?)
The Beach Boys (and a lot of other Fifties and Sixties bands that my Dad likes)
Alvin and the Chipmunks
The Grateful Dead had 2 full time lead singers. Jerry Garcia & Bob Weir each had their own songs, and alternated during live performances.
The Allman Brothers- Gregg Allman sang most of the leads, but Dickey Betts sang Ramblin’ Man their biggest hit.
I remembered another one. K’s Choice. Most of the songs are sung by the chick, but her brother does the lead on some of the tracks.
Randy Bachmann sang a few Guess Who songs.
But the ultimate has to be the Eagles. Every single member of the band was a lead singer, and they traded off fairly evenly on lead vocals. I’d say Don Henley and Glenn Frey sang 75% of the songs, with Joe Walsh, Timothy B. Schmit, and (a couple of times) Don Felder singing the rest.