The first one that springs to mind is the Pastels'
Baby Honey

No valley too deep, no mountain too high.

Prince - "Erotic City"

"Big Cheese" (b-side to "Love Buzz) - Nirvana
"Arriba" (b-side to "House") - Babes In Toyland
"Dagger Moon" (b-side to "D.O.A.") - Dead Moon

Sade
Make Some Room

Keep Hanging On

Room 55

Janet Jackson
70's Love Groove

Accept Me

God's Stepchild

Don't
eva
let nobody tell you you ain't
strong enough

Get A Job ~ That English Beat
(B~$ide of Doors of Your Heart.)
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Does it count if the B-side is a song off the same album as the single? When I think B-sides I think of a non-album track.

The Fall - Pat-Trip Dispenser
The Cure - Throw Your Foot
RAMPAGE!

Much prefer I Saw Her Standing There to the A side, I Want to Hold Your Hand,

"Hard Times" (b-side to "I Was Made For Loving You") - KISS
"Mr. Speed" (b-side to "Hard Luck Woman") - KISS
"Keep the Glove" (b-side to "Freakscene") - Dinosaur Jr.
"Better Than Gone" (b-side to "The Wagon", notable for featuring Don Fleming on vocals in that short-lived lineup) - Dinosaur Jr.
Normal Is A Myth.

Revolution/Hey Jude - That's what you probably meant.

Your right I screwed up- it was Day Tripper not Revolution.
You may be right, I might be crazy, but it just may be a lunatic you are looking for!

Day Tripper/We can work it out - Beatles
Don't worry baby/I get around - The Beach Boys

The Beatles had several two sided hits 1964-1968. We Can Work It Out-Revolution is the one I remember most.
You may be right, I might be crazy, but it just may be a lunatic you are looking for!

Love street/Hello I love you - the Doors
London calling/Train in vain - the Clash

Au Pairs - It's Obvious
The Doors - The Crystal Ship
The Beatles - Rain, Eleanor Rigby, Strawberry Fields Forever, I Am the Walrus
Elvis Costello - (What's So Funny 'Bout) Peace, Love and Understanding
Stevie Wonder - Master Blaster (Dub)
Värttinä - ijö
Kate Bush - Moving
Jethro Tull - Teacher
Science doesn't care what you believe.

Thanks for the Youtube link so that I could hear 'Rain.' That's a good track that I've never heard before.

I was going to mention about him only appearing to have one front tooth. I think fell off stage at one time in his early career as well.

Filmed just after the future Sir Paul chipped a tooth in a biking accident. See 0:41.

Brilliant cut.
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I've just looked up the lyrics to 'Rain.' I think I can honestly say that I've never heard that one. A rare Beatles' track indeed.

.and along with that I gotta nod RAiN flip side to the fab's Paperback Writer.
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The Beatles' 'Baby, You're A Rich Man' (originally the B-side to 'All You Need Is Love').

17 by jethro tull

"Angie" - Tori Amos (b-side to "winter")