manfred mann "blinded by the light" is a good example. although not certain i'd call that a cover. manfred mann made the song famous so i'd say that's the definitive version...
there must be a fair number of these where a famous performer wrote a song that became well-known only when sung by someone else. todd rundgren and darryl hall come to mind with "love is the answer" and "everytime you go away" with them as writers for England Dan and JFC and Paul Young.
it's funny. i'm old so i think young people are ignorant about history.. but then i turned out when i thought teenagers didn't realize XXX song was a cover that i didn't realize what i thought was the original was already a cover.