Willie Nelson is probably at least as famous for doing covers as he is for writing songs, but he he definitely ‘established himself with his own original songs’, so fits the terms of the OP.
Stardust was at least one album that was all covers. (Probably there are more; this is the one I know of that is explicitly all covers).
Her zydeco version of Sunny Side of the Street is one of those can’t-not-dance songs for me. At the very least, it puts some pep in my step when I’m walking and it comes up on the playlist.
I’m currently listening to Ozzy Osbourne’s Under Cover.
Up next is Garbage Days Re-Regurgitated by Exhumed, though I don’t know how “established” you’d consider them.
Does Emerson Lake & Palmer’s Pictures at an Exhibition count as a cover album?
Holy crap! For years, I’ve thought that would be the coolest name ever for an album (it was Truman Capote’s first novel) and there it is! Good deal.
I came in to mention this one–it’s being played and played in my car CD player these days.
Joni Mitchell and Carly Simon each have an album of standards (Both Sides Now and Torch). Didn’t care for either of them, though.
Although still fairly early on in his career, Bob Seger was fairly well-known when he released Smokin’ O.P.'s in 1972. His version of Love the One You’re With is my favorite.
Well, Todd did half an album of covers, does that halfway count? On Faithful, he covers The Beatles, Dylan, Hendrix, The Beach Boys and The Yardbirds.
Phish famously covered Quadropenia, The White Album, and Remain In Light (those are the ones I know of, anyway) on their series of live albums.
I think I’m the only one in the world who actually likes Pat Boone’s In A Metal Mood. So sue me.
Bob Dylan released an album in 1973 called “Dylan.”
It’s filled with horrible covers like “Mr. Bojangles,” “Big Yellow Taxi” and “Can’t Help Falling in Love.”
Dylan didn’t want it to be released and it is rare. It has never been released on CD.
http://en.wikipedia.org/wiki/Dylan_(1973_album)
I paid $2 for the album at a small record store in Memphis in the spring.
Personally, I think that Petra Haden’s “The Who Sell Out” is almost as good as the original ( http://www.petrahadenmusic.com/discog.html )
Another entry in the catalogue: Jazz clarinetist Don Byron’s album of music by Mickey Katz, the comedy/yiddish songwriter. Don Byron has a lot of respect for Mickey Katz’s skills on the clarinet. Chaim Afen Range and Paisach in Portugal are some of my favourites on the album.
Shawn Colvin’s ‘Cover Girl’ is pretty great, esp ‘Naive Melody’ and '‘You’re Gonna Make Me Lonesome When You Go’
MiM
The Church did this with Box of Birds. “All the Young Dudes” by Bowie was the oddest choice-esp. since lead singer Steve Kilbey’s always been a big Bowie fan-he certainly could have made a better choice.
I saw her and her group “The Sellouts” sing it live at the Ford Theater several years ago. A wonderful evening…the crowd loved it.
Todd Rundgren does some covers, but only half an album at a time (Faithful, and a bunch of songs on Utopia’s Another Live) unless you count With a Twist, which is him doing bossa nova covers of his own material.
Firewater has an album of covers called Songs We Should Have Written.
Oh, and David Bowie’s Pin Ups.
Lyle Lovett’s Step Inside This House is a tribute to the (mostly) Texas singer-songwriters he learned from–some as colleagues, others as heroes who became colleagues. A fine album & a good way to send some royalty money the way of fine songwriters who have avoided stardom so far. Special emphasis on the tunes of legend Townes van Zandt & Walt Hyatt, of the even more legendary Uncle Walt’s Band; their royalties go to their estates. Plus two actual “folk” tunes.
Legendary songwriter though he was, Townes always included “covers” in his set. Hear some of them in Road Songs. How about “Dead Flowers”? Plus selections from Dylan, Springsteen & Joe Ely. And several tunes by Houston bluesman Lightnin’ Hopkins–a big influence.
Iced Earth had Tribute to the Gods
Six Feet Under (featuring former Cannibal Corpse vocalist Chris Barnes) had Graveyard Classics and Graveyard Classics 2, the latter of which is a remake of “Back In Black” by AC/DC.
Harry Nilsson and his Nilsson Sings Newman
Mark Kozelek did an album of AC/DC covers called “If You Want Blood”.
There’s a somewhat well known (but very small time) folk duo called Storyhill (which I love) that did an album of covers called “Duotones” after releasing 6 albums of their own songs (plus several live albums).