You name the group/artitst

David Bowie

Black Magic Woman

Genesis

Zombie

Donovan (and a host of others. Love the Terry Reid version.)

The Ghost In You

The Rolling Stones

Flying Purple People Eater 

Pink Floyd

Gallows Pole

Is it Blood, Sweat & Tears?

Lots more haunting song titles than I imagined...thanks for rising to the spirited occasion

AND NOW BACK TO THE REGULARLY SCHEDULED NAME THAT BAND...

The Ventures

The Night The Lights Went Out in Georgia

The Drifters

Let's Get It On

The Pretenders

Pieces of April 

Prince

Me & Mrs. Jones

Jethro Tull

We're an American Band 

Hank Snow, or Asleep at the Wheel

Here, There & Everywhere

MNLinda - I was actually thinking of Johnny Cash's version - it's awesome. I'll have to check out the ones you mentioned.

Steely Dan

Reflections Of My Life 

elimar - I did the same thing. I heard it on a TV show and I was running around going, "What's that song? I know that song!" I hadn't heard it in years! Then I used an app on my iPhone and caught it in the nick of time. I would have never remembered, like you said it was just a one-hit wonder, but I used to love it when it came on the radio! So I bought it on iTunes and I even still have the 45! It was by a band called Marmalade. Now that song is stuck in my head!

How about...

Thank You Falettinme Be Mice Elf Agin