I like what K.D. Lang does with what is arguably Cohen's most famous song:
However, this one captivated me the first time I heard it and remains my favorite:
A brief anecdote: While in Spain this past August, we visited a second hand English book store in Madrid. When the two young men working there, both native Spaniards, both in their 20s, learned we were from Canada, the first thing they said, in unison, was "Leonard Cohen." The two--the shop owner and his helper--adored his music and mentioned the names of several songs. "Have you ever heard 'Alexandra Leaving'?" I asked. They hadn't. I told them to check it out online and they assured me, as two Cohen fans to another, that they would.
Update: Leonard Cohen, my father, and me