Song covers that are better than the originals

BDP24, yes you are truly in a minority regarding Jimi's playing and his version of "All Along the Watchtower".  On multiple occasions Dylan has acknowledged that Jimi's version is superior to his.

"Superstition" is one of my favorite Jeff Beck solos, but his version is not better than the original.  There's a story that Wonder wrote the song specifically of Beck.

Otis Redding said "the girl stole my song".  Aretha's version of "Respect" is probably better.

I like Marianne Faithfull's "Sister Morphine" more than the Stone's version, but, I don't know which is the cover (Jagger and Faithfull co-wrote the song).

Peter Paul and Mary's "Leaving on a Jet Plane" is another decent cover.

I like covers that change the tempo and nature of the song radically. Though not better than the originals, I still like My Chemical Romance's uptempo "Desolation Row" and Nouvelle Vague's down tempo "Guns of Brixton."  For weird and fun, anything covered by Shonen Knife will be fun to hear once in a while.

Hoiiiiin

^Sorry about that, not sure how that happened.:-)
Many good ones mentioned above, a few questionable.
Sacrilege I know: but I prefer Stevie Ray Vaughn's cover of "Little Wing" to Jimi Hendrix's original.

Similarly, one 'Goner chose the well known Santana cover of Black Magic Woman over the Fleetwood Mac original.  A lot of people would agree, but not me.   Carlos Santana rounds off all of Peter Green's sharp edges, and I think that the song suffers for it.  YMMV.