I love the Concrete Blonde "Everybody Knows." I have it on the soundtrack album for "Pump Up the Volume." There are LOTS of terrific covers of Leonard Cohen songs. Mostly because the songs are well written, but it is also probably the case that his performance will not fit everyone's taste, so his version does crowd out contenders.
I particularly like an R.E.M. cover of "First We Take Manhattan."
I particularly like an R.E.M. cover of "First We Take Manhattan."