Keith sings lead on “Happy” too. Great song!
The actual title is “Little T&A.” The lyrics do contain the words “tits and ass,” so what airplay it got was pretty much limited to FM stations. 
Hallelujah, by Leonard Cohen, has received more popularity since a cover by Rufus Wainwright was in one of the Shrek films. I believe the soundtrack albums to Shrek have sold pretty well, so it kind of works.
Dave Davies sang a few for the Kinks. Actually had hit with “Death of a Clown.”
“Don’t Stop” and “You Make Loving Fun” were top ten singles off Fleetwood Mac’s Rumours, sung by Christine McVie. She also sang “Over My Head” on their prior eponymous album.
Again, though, Fleetwood Mac didn’'t have just one “lead singer” or one primary songwriter. Lindsay Buckingham, Christine McVie and Stevie Nicks all wrote a lot of songs and they all tended to sing lead on the songs they wrote.
If Mick Fleetwood or JOHN McVie had sung lead on a song or two, THAT would fit the category.
I don’t know much about The Eagles, but the guy who sang “I Can’t Tell You Why” didn’t sing much did he?
It was sung by bassist Timothy B. Schmidt, and was, in fact, the first time he’d sung the lead on an Eagles song. Reading Schmidt’s entry on Wikipedia, it sounds like he’s only occasionally been a lead singer throughout his career. He did sing lead on at least one other Eagles song: “Love Will Keep Us Alive” (from the “Hell Freezes Over” reunion album).
Schmidt joined Poco when Randy Meisner left the band, then joined the Eagles when Meisner left that band, as well.
As far as the band The Cars, I didn’t do this on purpose, but I realized I really like the songs that Benjamin Orr sings and can’t stand the ones that Rick Ocasek sings.
Benjamin Orr was definitely a better singer and he sang their first big hit, Just What I Needed. One of the reasons I loved that song when it first came out was I felt that the vocalist had a snotty and detached tone to his voice which was cool as hell sounding at the time.
Sorry he died too young.
Ben Orr is second on my list of, “What the? Seriously? That’s not someone who should be dead” list.
Phil Hartman of course being number one.
All of ABBA’s hits had been sung by their femal lead singers Agnetha & Frida until Does Your Mother Know?, sung by male lead guitarist Bjorn.
The drummer of The Commodores sang the lead on Brick House, not Lionel Richie. What is it with drummers replacing lead singers? BTW, I beleive his name was Clyde Orange. With a name like that, he totally should have been a lead singer.
Some people compare Fiona Apple to Clyde as a musical performer, but I just don’t hear it…
Kelly Keagy was actually their co-lead singer in the early days. He sang about half the songs from Dawn Patrol and Midnight Madness as well as “Sentimental Street”, their second biggest hit after S.C. He would even set up his drum kit sideways in concert so the fans could actually watch him sing.
No kidding. 
Al Jardine sang lead on only one Beach Boys hit — “Help Me Rhonda.” In that, he is in fact tied with Dennis Wilson, who sang lead on their cover of “Do You Wanna Dance,” which was a Top 40 hit (unlike, it seems, the majority of songs cited in this thread).
In addition to “God Only Knows,” which did make the Top 40 (#39), Carl Wilson sang lead on the Beach Boys Top 40 hits “Darlin,” “Wild Honey” and “I Can Hear Music.”
I’ll have you know that Brick House went to #5 in the States. I cannot vouch for the other songs in the thread.
I wouldn’t call that one of their big hits, but “With a Little Help From My Friends”, which Ringo also sang, ought to count. Though not a Beatles single, it is one of their better known and most loved songs.
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The British blues band Chicken Shack (still going, apparently) had their only top twenty hit with “I’d Rather Go Blind” in 1969. Instead of being sung by band leader, lead guitarist, and usual lead singer Stan Webb, it was sung by keyboard player Christine Perfect.
She later ceased to be Perfect by marrying John McVie, joining his band, Fleetwood Mac, and becoming one of their co-lead-singers (but she had not generally had that status in Chicken Shack).
“Lady Lynda”, which Al wrote (or ripped of from Bach, though with acknowledgement, I think) and sang lead on, was a hit in Britain. (Admittedly it might be one that many The Beach Boys fans would rather forget.)
The “Death of a Clown” single was released, and was a hit, as a Dave Davies solo record, not a Kinks song (although I believe it may also have appeared on a Kinks album).
I remember seeing him perform* it on Top of the Pops, when the DJ presenter mistakenly introduced him as “Ray Davies”. Dave howled out “You did that on purpose!” before going into the song.
*Actually, Top of the Pops performances were often lipsynced to the record. I do not know whether that was the case in this instance.
Sometimes in Winter-Blood, Sweat and Tears
Not David Clayton Thomas.