Mott the Hoople became famous for their cover of a Bowie song, All the Young Dudes, but they also did a great version of Lou Reed's Sweet Jane and I've always liked this cover of Doug Sahms's At the Crossroads from their debut album:

Couldn't find a link on the internet to Dee Cooper's rendition of the Champs classic Tequila, but it is a great guitar cover.

Not so modern since Beethoven,Mozart etc were considered artists creating their own material. In the 20th century the same was so with the blues and jazz artists.

With pop music, lets take Frank Sinatra for example. A great singer, a great performer. An artist-I wouldn't consider him so. Didn't create music, only sang other people's creations. Couldn't play an instrument either.

Not taking anything away from great performers like Sinatra et al. But I have more respect for true artists like Dylan, Lennon & McCartney and the rest.

Record companies loved the old days when they hired writers and composers to create songs and then assigned them to certain performers. This kept the performers and creators dependent on each other and both subservient to the music company. The old "Brill Building" method would have someone like Dylan trapped in a room writing songs while the music company hired some pretty boy to sing them. Not to mention the old racial aspect of creators like Little Richard writing Tutti-Frutti but the music company hiring Pat Boone to make the real money from it

I can agree with that. Most of my prejudice to a cover, isn't because it's a cover, it's because it's not the first I heard, or even if not that, just the version I like better. UB40 sings Red Red Wine waaaay better than Neil Diamond, and I like 90% of his music. It also happens to be the first version I heard. Shinead O Conner sings Prince's Nothing Compares to U better than he does, and again HUGE fan of Prince.

I don't think either artist is "less" of an artists for using someone else's creation. As a listener, I just like what sounds good, whether it be a cover or not.

Untrue.  Completely and epicly untrue.  Untrue on a a mind-bogglingly massive scale.  

Beethoven wrote his own material.  He didn't perform it.  

Blues musicians didn't think in terms of "cover songs" at all - Lines, riffs and songs were borrowed from other performers and re-combined into new arrangements, but it wasn't even really considered a new song.  It's probably easier to think of blues song-writing  as an offshoot of the oral storytelling tradition.  Performers weren't writing their own songs so much as putting a personal spin on what was already there.  A lot of Robert Johnson's influence comes from the fact that the verses of his songs were  related to each other, rather than whatever the individual performer felt like singing at the time.  

Certainly, at the VERY top of the first-half-of-the-twentieth-century jazz food chain (your Louie Armstrongs, your Duke Ellingtons) the performers would write and copyright much - not anywhere close to all, but a fair ammount - of their own material.   But that was true for only a tiny fraction of jazz bands, the rest re-interpreting a pool of standards.  Even into the '60s, Miles Davis was "covering" Spanish composer Joaquín Rodrigo on Sketches of Spain, and one of Coltrane's best known songs was My Favorite Things.  The SONGS didn't matter as much (especially in the latter case) except that they served as raw material for extended improvisation.  

And then there's the Brill Building, which you mentioned.

I think that musicians performing there own material is trendy now, and has been for a measly couple of  decades, but I figure it'll go away again soon and music'll return to the way it was for the millenia before that, with the performer and the writer/composer being different folks.  And music will probably be all the better for it.  

Next up: Reptisaurus! decries the unpopularity of plagiarism among writers of prose & poetry.