"Totally agree with Fat B***ard on Aretha Franklin's version of Respect."

It probably bears mentioning that Aretha not only sang ("covered") Otis Redding's composition, she also wrote a whole additional "bridge"-type section of the song, the part where she spells out R-E-S-P-E-C-T. (The background singers' "Sock it to me" part was also new in Aretha's recording, not heard earlier.)

Otis, by the way, wrote a lot of his own material, and co-wrote even more of it with Steve Cropper, but we don't generally think of him as a "singer-songwriter," although that's pretty much excatly what he was. But he did "cover" many other songs, including some old "American Songbook standards" to which he applied a whole new style.

A favorite Otis Redding cover song: "Try a Little Tenderness."

Several Judy Collins recordings have been mentioned; let me add yet another, one which served as the title song for an excellent album: "In My Life" (a John Lennon song, of course ~ although nominally Lennon-McCartney).