Other artists singing The Smiths' songs  

The Psychodelic Furs also did a cover of "How Soon is Now". It's the version that they use for the show Charmed.

Reel Big Fish covered "Ask"



Jeff Buckley covered "I know it's over" and "The Boy With the Thorn in His Side"

Eurythmics - "Last Night I Dreamt That Somebody Loved Me"

Placebo covered "Big Mouth Strikes Again"

Belle and Sebastian covered "Girlfriend in a Coma" and "The Boy with the Thorn in His Side"

Antrhax - "London"

Death Cab For Cutie - "This Charming Man"

Royksopp - "There Is a Light That Never Goes Out" (they also do that song for the Geico caveman commercial)

Pete Yorn - "Panic"

"Please Please Please Let Me Get What I Want" has been covered by Third Eye Blind, Muse, The Deftones, Dream Academy, and Weezer

Coldplay - "Stop Me If You Think You've Heard This One Before"

Mark Ronson has done a version of Stop Me If you've heard This One Before. It's just about ok as club tracks go but pretty bland. Sounds vaguely like Gnarls Barkley (but not as good) and includes part of the tune of It Keeps Me Hanging on

http://www.myspace.com/markronson

I also know that Death Cab for Cutie have done a version of This Charming Man, as have Stars.

Both versions are really really different.