“About a Girl,” Nirvana
“The Bad Touch,” Bloodhound Gang
“Basket Case,” Green Day
“Bedtime Story,” Madonna
“Big Log,” Robert Plant
“Bullet with Butterfly Wings,” Smashing Pumpkins
“Clint Eastwood,” Gorillaz
“Dirty Harry,” Gorillaz
“Elderly Woman Behind the Counter in a Small Town,” Pearl Jam
“Empire State of Mind,” Jay-Z
“Epic,” Faith No More
“E-Pro,” Beck
“Everybody’s Everything,” Santana
“Feel Good Hit of the Summer,” Queens of the Stone Age
“I Write Sins, Not Tragedies,” Panic! At the Disco [and almost every other song of theirs]
“Interstate Love Song,” Stone Temple Pilots
“Jack-Ass,” Beck
“Jumper,” Third Eye Blind
“Kids,” MGMT
“Laid,” James
“Let It Rock,” Chuck Berry [Sings “Let It Roll” instead]
“Love Missile F1-11,” Sigue Sigue Sputnik
“Love Vigilantes,” New Order
“New Speedway Boogie,” The Grateful Dead
“Pompeii,” Bastille
“Pop Song '89,” REM
“The Rain, the Park and Other Things,” The Cowsills
“The Rockafeller Skank,” Fatboy Slim
“Strawberry Letter 23,” The Brothers Johnson [although “Strawberry Letter 22” does get mentioned]
“Suite: Judy Blue Eyes,” Crosby, Stills and Nash
“Synchronicity II,” The Police
“Valotte,” Julian Lennon
Amazing, I never thought there were so many songs that didn’t have the title in the lyrics. However, after looking through the list I can find only 8 songs that I have heard of before. All the rest are completely unknown to me.
Actually, I have only heard of roughly 80% of the artists. This is an indication of how little I listen to music. Most of the music on my PC is main stream pop from the 50’s and 60’s and country music from pre 1980. When I’m driving I listen to talk back radio or a cricket commentary. I never listen to music while in the car. This explains my ignorance in these matters.
“Several species of small furry animals gathered together in a cave and grooving with a Pict” - Pink Floyd (I suppose one could argue that it doesn’t have lyrics at all, but it does have words).
“Astronomy Domine” - Pink Floyd.
Also by R.E.M.
Texarkana
Country Feedback
Good Advices
I just read an interview with Justin Hayward of the Moody Blues where the interviewer twice refers to “Legend of a Mind” as “Timothy Leary’s Dead.” Hayward, tactfully, doesn’t bother to correct him.
Well, it’s not Hayward’s song anyway.
“Ray’s not in the band anymore anyway, so screw 'im.”
Plus
I Don’t Believe You
Any Talking Blues
Any Dream songs
Any I Shall be Free songs
While Highway 61 appears in Highway 61 revisited. revisited does not.
Bohemian Rhapsody.
While my list was far from complete, I consciously excluded songs where a key word or phrase from the title does appear in the song, such as “Temporary Like Achilles” or “Queen Jane Approximately.”
Every song ever written by Der Blutharsch, Muslimgauze, Orrery and… Well, really too many to mention.
Also: Mayhem’s De Mysteriis Dom Sathanas.
Nirvana has already been mentioned, but I believe “Smells Like Teen Spirit” is a particularly well-known example.
Wigwam. One of countless words that are not heard in the song.
You’ve got to hand it to ol’ Zimmy, the man has brass balls. Who would have predicted in the '60s that he of all people would have a hit single with no lyrics?
“Summer, Highland Falls,” Billy Joel
I’m just going through Christmas songs since I’m practicing them.
The Christmas Song
Twelve Days of Christmas (in the song, it’s “twelfth day.”)
The Little Drummer Boy
The Chipmunk song (apparently not called “Christmas Time Is Here”)
Carol of the Bells
Those are the ones that come to mind.
Note that almost all of these songs are somewhat old – I think the only one from the last 10 years that someone’s mentioned so far is “Pompeii.” One of the local radio stations has a weekly music business show. I heard part of an episode that said this is intentional – the business people want customers to be able to easily find the song on YouTube, Spotify, etc.
A list of recent singles without the title in the lyrics would be very short. Tove Lo’s “Habits,”* Kanye West’s “Black Skinhead” and the aforementioned “Bastille” are all I can think of, and I’m a pretty big fan of pop music. (Well, technically Taylor Swift’s “We Are Never Ever Getting Back Together” qualifies, since every occurence of the title phrase contains 2, 3, or 0 "ever"s.)
*or, in full, “Habits (Stay High)” – so that might not even count, depending on how you feel about subtitles
Classical Gas 
Overture by the Who. ( It does have lyrics at the end. )
Several Species of Small Furry Animals Gathered Together in a Cave and Grooving with a Pict - Pink Floyd