My recollection:
American Pie - Don McLean
Bohemian Rhapsody - Queen
Cecilia - Simon & Garfunkel
Young enough that I didn’t know what a “levee” was, nor what the line “making love in the afternoon” (Cecilia) meant.
It was very likely C.W. McCall’s “Convoy.” shudder
Sugar sugar by the Archies. Followed by anything on a K-Tel record.
Probably the entire “Goodbye Yellow Brick Road” album.
I fixated on that when I first really started listening to music.
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Funny, my kids asked me what was the song I got sick of due to overplay when I was their age, so we found this one on the web…they made me shut it off after about two minutes.
“Puttin on the Ritz” by Taco
“Coming to America” by Neil Diamond
The local radio station came to our local pool and handed out 45s to all the kids. My brother got Taco, I got Neil. We played the heck out of those records, and I memorized each! I was probably 4 years old.
I am really fixated on lyrics and would guess that I’ve memorized thousands of songs since 
“Heart” from Damn Yankees. I sung it as part of a performance.
Since I grew up on Broadway show tunes, I picked up on lyrics early on and probably memorized others before that. I definitely memorized “Six Months out of Every Year,” too.
Probably the first one I learned was “The Sound of Silence”, because we sang it in elementary school choir. And no, I don’t have any delusions about our quality.
Later, I also learned the full lyrics for “Tequila” and They Might Be Giants’ “Minimum Wage”. Oh, and also for “Rock and Roll Part II”.
Not to mention the part about getting up to wash his face…
Well played, sir. Very well played. 
As for me, my memory is hazy. Probably either “Pleasant Valley Sunday” by the Monkees, or “Monster Mash” by Bobby “Boris” Pickett and the Crypt-Kickers.
Mad Magazine often had song parodies, and ‘Ground Round’ was sung to the tune of ‘Downtown’, so this was probably mid-1960s and I was in elementary school. I didn’t know all the words to Downtown, but still remember every verse of Ground Round.
I think I need this one explained to me; what am I missing?
My contribution: Camp Granada by Allan Sherman.
Hello Mudda, Hello Fadda.
mmm
Because his face was buried somewhere earlier :D.
I forgot about another tune…“Bad, Bad Leroy Brown”.
Wouldn’t It Be Nice (Beach Boys), Good Day Sunshine (Beatles), Ruby Tuesday (Stones)
This would have been in 1975, when I was five years old, but for some reason my parents were exposing me to music recorded in the year 1966.
The Flying Purple People Eater by Sheb Woolley
Little Arrows by Leapy Lee
You Can’t Roller Skate In A Buffalo Herd by Roger Miller
I was singing along with my mother to Engelbert Humperdinck at the tender age of four(ish). Not that I understood half of it but she played it so often I guess I just learned it by rote (?) Maybe that doesn’t count. I also had a lot of soundtrack albums and the next one that comes to mind is 101 Dalmations. Especially Cruella De Ville.
It might have been Nervous Norvus’ “Transfusion” (“Put a gallon in me, Allen”).
There was also “Susie Q”, with all its rich symbolism and emotional complexity.
My earliest memories were through Beatles tunes, so maybe “Lucy…” or the title track.
Huh. Is this the consensus of what he meant? If so, I’ve missed it for 47 years.
mmm
I can still sing every word of every song on Styx Paradise Theater. Growing up, I didn’t get to listen to pop much because dad played be-bop jazz whenever he was home.