Some fantastic picks here! Some I'm familiar with and some are new to me.
This Mortal Coil is one of my favorite acts and also one of the great cover bands IMHO - especially their Big Star covers.
Along the lines of Hendrix's All Along the Watchtower, one of the best covers of all time has to be Led Zeppelin's version of In My Time of Dying:
Like Hendrix's it's a Dylan cover - and like Hendrix's it's more famous than the original (and far superior).
Also, Eliott Smith's cover of Big Star's "Thirteen" is so very beautiful: