Peter Murphy had a college-radio hit with a song* that sounded like a lawsuit with the names “Matt Johnson [The The]” and “Uncertain Smile” all over it.
Nah, Eric Carmen’s song is the one that sounds just like Rachmaninoff’s Piano Concerto No. 2 in E-minor. 
Why Don’t You Get a Job by the Offspring almost invariably turns into Cecelia by Simon and Garfunkel in my brain.
“Stay” by 60ft Dolls and “Hey Jealousy” by the Gin Blossoms
“Hush”, Deep Purple
“A Day in the Life”, Beatles (the second half of the middle section)
Both came out in 1967…does anyone know which was released first? If they were released within a few months of each other, I doubt one band could have heard the other in time to record their version…I guess it was just something in the (English) air.
As long as we’re going there, let’s not forget “I Want a New Drug” and “Ghostbusters!”
Also:
“Viva La Vida” and “If I could Fly”.
“Dani California” and “Mary Jane’s Last Dance”
California Dreamin-Mommas and Poppas
Don’t Fear the Reaper-Blue Oyster Cult
They go well together
“All Day and All of the Night” by the Kinks and “Hello, I Love You” by the Doors.
Twist And Shout = La Bamba
My wife always sings the first line of the chorus of The Contours “Do you love me?” followed by the second line of The Isley Brothers “Twist and Shout”.
Bob Marley & The Wailers’ “Buffalo Soldier” & The Banana Splits Theme song.
George Harrison’s “My Sweet Lord” is so much like the Chiffon’s “He’s So Fine” that the songwriters sued him successfully for plagarism. And then they recorded “My Sweet Lord.”
Never noticed it before but, yeah.
Also “Goin’ Up the Country” by Canned Heat and “A Good Feelin’ to Know” by Poco.
Actually, the Deep Purple version was recorded in 1968, but the original by Billy Joe Royal was from 1967, and does contain the same “na-na-na-na” riff. For a trifecta, add the ending of “Surf’s Up” by the Beach Boys.
The theme from The Smothers Brothers Comedy Hour and “Love and Marriage.”
Really? Ray Davies was going to sue, but decided not to bother.
“Rocket Man” makes me think of “Space Oddity”. Both are about men riding rockets into space, and both were produced by Gus Dudgeon.
“Benny and the Jets” reminds me of both “Changes” (the stuttering refrain) and “Ziggy Stardust” (songs about fictional front men/women).
So now pretty much any Elton John song makes me think of David Bowie.
The melodies are sort of similar, but “Reaper”'s got too much cowbell.
How about Smells Like Teen Spirit & More Than A Feeling?
Not because of the lyrics or melody, but I always expect to hear Somebody to Love after White Rabbit. It’s because I own the 45 and usually play 'em both together.
There are also a bunch of other songs that I expect to follow each other, courtesy of KTel!
When I hear Pachelbel’s Canon in D. I sing “Jolly Old Saint Nicholas”.
And when I hear the Final Jeopardy music, I sing “I’m a Little Teapot”.
And, pursuant to what zoogirl just said, you’re not allowed to play CSN’s Suite: Judy Blue Eyes without immediately following it up with Marrakech.
Also At the Zoo must follow Hazy Shade of Winter (Simon and Garfunkel), and Elton John’s Funeral For a Friend isn’t finished until you’ve played Love Lies Bleeding.
Finally, The second half of Queen’s We Will Rock You is We Are The Champions.