i love billy bragg's version of "jeanne."
here are some other good ones:
kirsty maccoll - "you just haven't earned it yet, baby"
sandie shaw - "hand in glove"
sandie shaw was a great '60s british singer, sort of like the british dusty springfield. she made three solid albums, all in the '60s, before reappearing in the '80s. morrissey was a big fan of hers and i think spurred her on to cover "hand of glove." she made a record for rough trade in 1988, and i think the jesus and mary chain were on a couple of tracks, but i could be wrong.
i also have an EP by a ukrainian band called (surprisingly) the ukrainians, which consists of four smiths songs done in russian. the four songs are "the queen is dead," "bigmouth strikes again," "what difference does it make?" and "meat is murder." it's actually pretty fucking awesome.