It's rare when you find covers that actually are better than the original song but I've found some:

Britney Spears - I Love Rock'N'Roll
Britney Spears - My Prerogative
Shakira - Waka Waka (Time For Africa)
Jennifer Love Hewitt - The Difference Between Us
Glee Cast - Total Eclipse Of The Heart
Jessica Simpson - Angels
Jessica Simpson - These Boots Are mAde For Walkin'
Jessica Simpson - Take My Breath Away
Leona Lewis - I Will Be
Shakira - Islands

What's yours?

Hallelujah - Jeff Buckley (original by Leonard Cohen)

The only cover song I know which turned out to better than the original version.

Leona Lewis - Run.
Mark Ronson Feat. Lily Allen - Oh My God.

Az Yet - Hard To Say Im Sorry (Chicago sings the original)

Does this include if they sample a song?

Anyway...
Whitney Houston - I Will Always Love You
Mariah Carey - I'll Be There
Beyonce - At Last

How could I forget?

Ashlee Simpson - Invisible

Leona Lewis - Run? Mmm no, i prefer Snow Patrol's

Ashley Tisdale - Time After Time
Britney Spears - I Love Rock 'N Roll
Leona Lewis - Run
Leona Lewis - I Will Be

Silversun Pickups - Creation Lake
William Fitzsimmons - I Kissed A Girl
William Fitzsimmons - Heartless

Beyonce- Entire Cadillac Records Soundtrack

Evanescence - Thoughtless
No Doubt - It's My Life

It's "Total Eclipse of The Heart"


I think everyone has said what I would have said besides a few

Thank you for correcting me, it's stupid coz I had the name on my front

Leona Lewis - Run
Britney Spears - My Prerogative

Leona Lewis - Run
Charice - Note to God
Whitney Houston - I Will Always Love You

Britney Spears - My Prerogative
Britney Spears - I Love Rock n Roll
No Doubt - It's My Life

Leona Lewis - I will be, Run
Ashley Tisdale - Time After Time, Last Christmas, Kiss The Girl, Never Gonaa Give You Up, Don't Touch (The Zoom Song)
Amy Diamon - Underneath Your Clothes
Beyonce - Honesty
Carrie Underwood - I'll Stand By You
Glee Cast - Alone, Total Eclipse Of The Heart, I Dreamed A Dream, Faithfully, Don't Stop Believin' , Take A Bow, Home,Maybe This Time, Somebody To Love, Don't Rain On My Parade and Run Joey Run.
Miley Cyrus - Every Rose Has It's Thorn, One In A Million, These Four Walls, Dream.
Jennette McCurdy - Homeless Heart
Kris Allen - Heartless
Mariah Carey - Endless Love, I'll Be There,Without You,I Want To Know What Love Is.
Rihanna - Te Amo, Goodbye.
Susan Boyle - Wild Horses, The End Of The World.
Vanessa Husgens - Whatever Will Be, Colors Of The Wind.

Pet Shop Boys, "Always on My Mind"


Cyndi Lauper, "Money Changes Everything"


Art of Noise featuring Tom Jones, "Kiss"


Johnny Cash, "Hurt"


These are the first few I could think of off the top of my head.

Chaka Khan - I Feel For You
Prince - Betcha By Golly Wow
Phyllis Hyman - Betcha By Golly Wow
Cat Power - Wild Is The Wind
Nina Simone - Wild Is The Wind
George Michael - Wild Is The Wind
The Fugees - Killing Me Softly With His Song