There's the original, then a cover version that's almost as famous (or more), then there are these ones.
1: All Along the Watchtower by U2
Original: Bob Dylan
Best Known Cover: Jimi Hendrix Experience
I think U2's faster tempo lends an urgency to the song that improves the atmosphere. I kind of like Bono's improvisation ("All I need is red guitar...")
2: Respect by Diana Ross and the Supremes Join the Temptations
Original: Otis Redding
Best Known Cover: Aretha Franklin
3: When The Levee Breaks by Playing for Change (featuring John Paul Jones)
Original: Memphis Minnie
Best Known Cover: Led Zeppelin
Every Playing For Change (a collaboration of artists all over the world contributing their talents - often with flavours of their local culture) is epic. The Led Zeppelin version is not the original, though it is better known and informs this version.
4: Hound Dog by Karis Eden
Original: Big Mama Thornton
Best Known Cover: Elvis Presley
5: 20th Century Boy by Chalk Circle
Original: T.Rex
Best Known Cover: Placebo
The Placebo version came up first in my search, and I saw them do this live on TV with David Bowie, so I'll count that as better known. I think the Chalk Circle version has more 'oomph'.
6: I Fought The Law by Green Day
Original: Bobby Fuller Four
Best Known Cover: The Clash
7: Nothing Compares 2 U by Toni & Chris Cornell
Original: Prince/The Family
Best Known Cover: Sinead O'Connor
Chris Cornell released a version of this song after Prince's passing, but knowing now that Chris himself would pass on himself a year later, I've chosen this heartbreaking version with his daughter Toni in a duet instead.
8: 99 Red Balloons by Goldfinger
Original: 99 LuftBallons by Nena
Best Known Cover: 99 Red Balloons by Nena (English Version)
By changing the language of the lyrics, Nena covered themselves (in my books). So Goldfinger gets 2nd place.
9: Wild Horses by Chantal Kreviazuk
Original: The Rolling Stones
Best Known Cover: The Sundays
The Sundays version and any other female artist with an airy voice will draw comparisons. I picked Chantal since she's one of my favourite singer/songwriters.
10: Sweet Child O'Mine by Rachelle Spring
Original: Guns N Roses
Best Known Cover: Sheryl Crow
A Bossa-Nova version???? Sacrilege some might say, but you have to admire the audacity.
11: Angel From Montgomery by Leslie Spit Treeo
Original: John Prine
Best Known Cover: Bonnie Raitt
There's a million versions of this song that vary between country, blues or even jazz. This one from a Toronto band is rock n' roll.
12: Dancing in the Streets by Van Halen
Original: Martha Reeves and the Vandelas
Best Known Cover: Mick Jagger and David Bowie
I don't know what kind of witchcraft Eddie Van Halen was up to...