Sort of inspired by this thread. Looking for songs where the title is sung absoutely first.
Suzanne–Leonard Cohen
She Loves You–The Beatles
Simbleshanks the Railway Cat–Cast of CATS
“Why Don’t We Do It In the Road” by the Beatles
“This Song’s Just Six Words Long” by Weird Al
Isn’t “When” the first lyric of “Suzanne”?
ETA: Never mind, I’m familiar only with my folksinger sister’s cover of the song, not the actual Cohen version, to which this does not apply.
*Yesterday *– The Beatles
Five to One – The Doors
She’s Got a Way – Billy Joel
Hey You - Pink Floyd
Here Comes The Sun - The Beatles
“Tequlia” The Champs
“Wipe Out” The Surfaris (assuming maniacal laughter doesn’t qualify as a lyric)
More seriously…
“God Save the Queen,” The Sex Pistols
Hey Jude… The Beatles seem to dominate in this area!
Quite a few of the old standards:
Summertime
All of Me
Fly Me to the Moon
Come Fly with Me
A Fine Romance
I’ve Got You under my Skin
Blue Moon
Some Enchanted Evening
Climb Every Mountain
Edelweiss
…and many, many more, as they say.
“Everything’s Changing” – Kak
“If I Had a Boat” – Lyle Lovett
“We’re In the Money” – various
“The Lady in Red” (from 1935) – various
“Bow Tie Daddy” – the Mothers
“Dear Doctor” – Rolling Stones
“White Bird” – It’s a Beautiful Day
“Love of My Life” – Queen
“Dear Diary” – The Moody Blues
“Cool Brittania” – Bonzo Dog Band
“Hello Mabel” – Bonzo Dog Band
“By a Waterfall” – various
“She Came in Through the Bathroom Window” – Beatles
“Mean Mr. Mustard” – Beatles
“Her Majesty” – Beatles
“Is You Is or Is You Ain’t My Baby” – Louis Jordan
“Only You Know and I Know” – Dave Mason
TEQUILA!
Some Blondie tunes:
One Way Or Another
I’m On E
The Tide Is High
Some Chic/Rodgers/Edwards goodness:
Good Times
I Want your Love
We are Family
Everybody Dance
Disco rules!
Happy Birthday
Every Gilbert and Sullivan song.
Jingle Bells
Onward Christian Soldiers
Rock of Ages
Day by Day
The Mashed Potato by The Undertakers.
Dave Matthews Band - Don’t Drink the Water
The Beatles - Dear Prudence
The Delgados - I Fought the Angels
Does It Offend You, Yeah? - Let’s Make Out
Florence + The Machine - I’m Not Calling You a Liar
Florence + The Machine - My Boy Builds Coffins
Hot Chip - Bendable Poseable
I Mother Earth - Not Quite Sonic
I Mother Earth - One More Astronaut
Janet Jackson - So Much Betta
Jeff Buckley - Eternal Life
Kanye West - Flashing Lights
Manic Street Preachers - I Think I Found It
Manic Street Preachers - Your Love Alone Is Not Enough
Manic Street Preachers - Rendition
Moloko - Sing It Back
No Doubt - Hey You
Pearl Jam - Johnny Guitar
Pearl Jam - Down
Pearl Jam - In the Moonlight
Pearl Jam - State of Love and Trust
The Polyphonic Spree - Light and Day
Rammstein - Weisses Fleisch
Rammstein - Bestrafe Mich
Rammstein - Bück Dich
Scissor Sisters - Laura
Tripping Daisy - I Got a Girl
The White Stripes - Dead Leaves and the Dirty Ground
That was fun. 
The Beatles - It Won’t Be Long; Lady Madonna; Eleanor Rigby; Lovely Rita; Help!; I’ve Just Seen A Face; There’s A Place; Can’t Buy Me Love; Martha My Dear
Breathe and* Money*, both off The Dark Side of the Moon.
“Almost Cut My Hair” - Crosby, Stills, Nash & Young
“Sit Down I Think I Love You” - Buffalo Springfield
“Do I Have To Come Right Out And Say It” - Buffalo Springfield
“Eight Miles High” - The Byrds
“Oye Como Va” - Santana
“Mona” - Bo Diddley
“Truckin’” - Greatful Dead
“Sugar Magnolia” - Greatful Dead
So close:
[Got a] Black Magic Woman - Fleetwood Mac
[Listen to my] Bluebird [laugh] - Buffalo Springfield
No, that begins “Oh, help me please, Doctor, I’m damaged.”
Isn’t the first line “I look at all the lonely people”?