I get all of these songs confused in my mind:
“Stay” - Pink Floyd
“Day After Day” - Badfinger
“Summer Breeze” - Seals and Croft(?)
Surely someone can suggest a few more ditties for me to mutually confuscate over?
Since you mention “Day After Day,” I always hear Joe Jackson’s “Breaking Us in Two” as a borrowing of that song.
Prince 1999 and Phil Collins Sussudio
The Doors “Hello I Love You” & The Kinks “All Day And All Of The Night”
Nice one, Annie!
Thank you. Me also.
“Hello, I Love You” by the Doors.
“Destroyer” by the Kinks (which I thought until now was titled “Paranoia Will Destroy Ya”), and also by the Kinks-
“All Day and All of the Night”
(I also just saw that Destroyer deliberately references Lola & All Day.)
Listen close to how Beethoven’s 9th, the Chorale, reworks themes in Bach’s Jesu, Joy of Man’s Desire.
And now I see Annie chimed in also! 
Reach by S Club 7
Lust For Life by Iggy
Cat Stevens Father and Son & The Flaming Lips Fight Test
The opening of “Lust for Life” always makes me think of the opening of Adam Ant’s “Goody Two Shoes”.
Other sound-alikes, especially the main guitar licks: Edgar Winter’s “Frankenstein” and ZZ Top’s “Cheap Sunglasses”.
At least, that’s what the judge said.
A friend of mine made a mixtape with Lust for Life bumping up against Town Called Malice by The Jam, and I couldn’t tell where one stopped and the other began!
Possibly too obscure and ill-defined, but I hear TISM’s “I Rooted A Girl Who Rooted A Guy Who Rooted A Girl Who Rooted A Guy Who Rooted A Girl Who Rooted Shane Crawford” every time I hear the commercial (Target? HSN?) with the song that goes “… a picture of me, a picture of you”.