From 1970 and Loaded (perhaps on balance their best album, although we can argue that another time) please enjoy the latter day Velvet Underground and the suave vocal stylings of Lou Reed on their unlikely but ubiquitous rock anthem "Sweet Jane."
And from 1988, and their equally unlikely indie-rock left field smash hit The Trinity Session, please enjoy Cowboy Junkies, featuring the languid vocal stylings of the lovely Margo Timmins, and an ineffably laid back cover of same.
BTW, the Velvet's track above is the uncut version, with the "heavenly wine and roses" bridge that was excised -- to Lou's ire -- from the original album version and as a result from just about everybody else's subsequent covers. I myself am of the opinion that the song plays stronger without it, and Lou has gone back and forth on that when he performs it himself. I forget whether he sang it on the Velvet's live reunion album from 1993, but I'm pretty sure he did at the concert for the opening of the Rock and Roll Hall of Fame in '95 (backed by Soul Asylum no less).
As for the Cowboy Junkies version, all I can say is that it makes me very, very sleepy, like most of their stuff. In their defense, however, it's a cover of the equally languid version on 1969: Velvet Underground Live, an album that I've always thought of as The Velvets in a Mellow Mood For Lovers Only. In any case, I've had a huge thing for Margo Timmins for the longest time, so my critical objectivity is by definition suspect.
As for the song itself, it's funny to think of it, but by now, "Sweet Jane" has probably been covered more times by more different people than "Johnny B. Goode."
Okay, maybe not more times, but close.