I'm a big fan of the Kay Starr version

Here's what I play for the intro/verse (capo up to 5th fret to do it in D like the recording)

       Am    Bdim7             Am/C Dm
Now gather 'round while I elucidate

       Am/E       Dm/Bb    Am Bdim7 Am/C E7 (last 4 chords are the turnaround)
'bout what goes on when it   get's      late

the last line "in the night" holds on a CMaj7#5 and a walking bass

the Chorus is something like this
                Am                E7          Am    E7
When the spooks have a midnight Jamboree
Am                            Dm       E7
They break it up with fiendish glee
Bdim7                           Am
Ghosts are bad, but the one that's cursed
          E7                                          Am
It's the Headless Horseman, he's the worst


and then

C7
With a hip-hip hop and a clippity-clop
                                  F7         G7
He's out looking for a head to swap
C7
So don't stop to figure out a plan
                                                 E7
You can't reason with a headless man

and back to the intro/verse pattern