Funeral for a Friend/Love Lies Dying - Elton John
Tainted Love/Where Did Our Love Go? - Soft Cell
Another One Bites the Dust/We are the Champions -Queen
Others?
Feeling That Way / Anytime – Journey
Heartbreaker / Living Loving Maid (She’s Just A Woman) - Led Zeppelin
You Never Give Me Your Money / Sun King / Mean Mr. Mustard / Polythene Pam / She Came In Through the Bathroom Window / Golden Slumbers / Carry That Weight / The End - The Beatles
“Goin’ Out of My Head / Can’t Take My Eyes Off You” by the Lettermen. In all cases, I believe these songs were released as two songs on one side of the same record, so it would’ve been harder for them NOT to be back-to-back.
I think you mean We Will Rock You / We Are the Champions. 
And, in answer to Prof. Pepperwinkle, at least in this case, the two songs were released as a double-sided single, one song on each side of the 45. On the album, they’re adjacent tracks.
Eruption / You Really Got Me - Van Halen
Night Flight to Venus/Rasputin - Boney M
Derp.
Sgt. Pepper’s Lonely Hearts Club Band / With a Little Help From My Friends - The Beatles
Foreplay/Longtime - Boston
The Load Out/Stay - Jackson Browne
The obvious ones are those which segue into one another on the original album. A number have already been mentioned… here are some more:
Peace Frog/Blue Sunday – the Doors
Sgt. Pepper’s Lonely Hearts Club Band (reprise)/A Day in the Life – the Beatles
Help on the Way/Slipknot!/Franklin’s Tower – Grateful Dead
Glad/Freedom Rider – Traffic
I was going to post this but got totally distracted when I found out that is not Peter Cetera singing with Steve Perry. I was so sure! :eek:
Sirius/Eye in the Sky - Alan Parsons Project.
Hard to Say I’m Sorry/Get Away – Chicago (though that second one doesn’t get played nearly often enough)
Pink Floyd has several
Happiest Days of Our Lives/Another Brick in the Wall pt. 2
Brain Damage/Eclipse
Empty Spaces/Young Lust
Of course that tends to happen when you start breaking up concept albums.
Space Intro/Fly Like an Eagle - Steve Miller Band
Saint Stephen/The Eleven - Grateful Dead
And back several years ago I noticed that the local country station almost always followed Proud to be an American with Ol’
Red for some reason.
Don’t Want You No More/Not My Cross To Bear – Allman Brothers
Bleeding.
Excuse me.
Bleeding.
Also:
Crosby, Stills and Nash Suite: Judy Blue Eyes/Marrakesh
Simon and Garfunkel A Hazy Shade of Winter/At the Zoo
Reminder to DJs: if you’re not playing these pairs as a single track, you’re doing DJ’ing wrong, and need to turn in your turntables.
Lights / Stay Awhile - Journey
The Star-Spangled Banner / O Canada
O Canada / The Star-Spangled Banner
John Entwistle: I Believe in Everything/Rudolph the Red Nosed Reindeer.
The Beatles: You Never Give Me Your Money/Sun King/Mean Mr. Mustard/Polythene Pam/She Came In Through the Bathroom Window/Golden Slumbers/Carry That Weight/The End/Her Majesty