A Cover Riddle

Today's theme is "Guess the Theme"...
Riddle me this: What do the following tunes all have in common?

Little Richard - Brown Sugar [originally by the Rolling Stones]
Try to imagine Little Richard covering the Rolling Stones and you'd be 100% right. This cover brings a big grin to my face at precisely the 18-second mark.

Me First & The Gimme Gimmes - Fire & Rain
[originally by James Taylor]

Madonna & Warren Beatty - Now I'm Following You (Part I)
Catchy tune from Madonna's album I'm Breathless, which served as a soundtrack to Dick Tracy (hence Beatty's guest vocals). News to me, but Madonna's massive hit Vogue was originally from this album.

Mr. Big - Wild World [originally by Cat Stevens]

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That shouldn't be too hard, methinks.
I'll post the answer in a few days in the form of a cover.